Some questions on /r/AskHistorians are difficult to answer, because the answer is probably 'we don't know'. And while reaction videos may be popular on YouTube, and people asking questions here very commonly want to know how people reacted to this or that...writers in the past just don't focus that much on what other people thought of things. So the chances of this having an answer is not high. Of course, maybe if I looked at some obscure journal article written in German in 1946, I'd discover what Freud's mum thought of his theories. Maybe I'm missing something embarrassingly obvious (I hope not!). But we don't know is probably the answer here.

Considering the centrality of the mother-child relationship to Freud's theorising, there's quite a lot of discussion of their relationship when Sigmund was a child. But there's really very little research into Freud's relationship with his mother (called 'Amalia' on her gravestone, but mostly called 'Amalie' in the family) when they were adults. There's even fewer that I can currently access; the book I'd want to have on me to answer this question (Freud's Women by Lisa Appignanesi and John Forrester) is in my office, and I've been working from home recently (but a look at the snippets that are available on Google Books suggests there is not that much about his mother as an adult in the book). The other book that I don't have access to that might be useful is Freud And His Mother by Deborah Margolis (published in 1977). Neither of the two letters in the 1960 Letters of Sigmund Freud addressed to his mother mention his theorising, instead being about life events. Certainly the big biographies of Freud (e.g., Peter Gay's Freud: A Life For Our Time) don't mention what his mother thought about his theories when they were both middle-aged or older - he was in his forties when he published his first big work, the Interpretation Of Dreams, and she was in her sixties. Such biographies are much more interested in Sigismund Freud's relationship with his mother when he was a child (perhaps for obvious reasons).

Freud himself seemed to both idolise and fear his mother, judging by his (really quite brief) discussions of his mother in his voluminous writings. He apparently felt a sense of freedom when she passed away. He doesn't seem to have discussed what she thought of his theories.

Another view of Amalie Freud - probably the most detailed - comes from Judith Bernays Heller (the daughter of Freud's sister), who discusses her remembrances of the family in an article published in Commentary in 1956:

My grandmother...had a volatile temperament, would scold the maid as well as her daughters, and rush about the house.

and

She was charming and smiling when strangers were about, but I, at least, always felt that with familiars she was a tyrant, and a selfish one. Quite definitely, she had a strong personality and knew what she wanted, and the best evidence of that is the way she held her two sons and five daughters together, in spite of all the divergences and differences in their interests and their temperaments. And she had a sense of humor, being able to laugh at, and at times even ridicule, herself. I remember her saying to me, when I was supposed to choose some present for myself from her cabinet, where she kept a few treasured antiques: “After all, the best antique in my house is myself, and me you cannot take.”

Judith Bernays Heller doesn't, in her memoir of Freud's parents, mention what they thought of his theories.

Freud was happy for his daughter Anna to become, basically, the most prominent keeper of his legacy after his death, so he wasn't opposed to women being practitioners of psychoanalysis, or having opinions about psychoanalysis. The impression you get from what is written of Freud's childhood is that his family largely kept to the tight traditional division of labour between the patriarch as the breadwinner (his father the successful wool merchant) and the matriarch as the head of the household within the household. Perhaps either she refrained from stating in public what she thought of the theory (if she thought about it at all - perhaps she had more important stuff to deal with, from her perspective), or nobody bothered to ask her (women's opinions were not always valued in the strongly patriarchal culture in that time and place - women did not get the vote in Austria until Amalie was eighty-four).

It's worth remembering, too, that Freud didn't think that male children wanted to sleep with their mothers, despite the pop culture impression of Freud. Instead, the Oedipal complex is much more metaphorical than literal - the child competes with the father for the mother's attention and love, and ultimately (given that Freud believed we are evolved beings whose behaviours ultimately derive from sex and survival, given the centrality of sex and survival to evolution) this competition is driven by biological drives which - later on, once puberty has occurred - also play a role in driving all that sexy sex stuff. So chances are that if he discussed his theories with her, he didn't present them in the salacious pop culture form of it, but rather as a relatively dry and technical theory of what causes mental illness.

...or maybe what she thought about her son's theorising is out there somewhere in one of the archives of Freud's papers and letters, and has simply never been translated into English (remembering that Freud grew up speaking German in Vienna)...or perhaps I'm missing something. It's hard to prove that negative - all I can say is that it does not appear to be widely known information available in every biography of Freud. In any case, Amalie Freud's opinion of stuff like the Oedipus Complex is, for better or worse, not seen as an important factor in Freud's biography.

It is extremely unlikely that Freud's mother Amalie Freud (née Nathanson) was unaware of his psychoanalytic ideas, but unfortunately nothing is known about her attitude to them.

None of his numerous biographers mention it (Jones 1953, Gay 1988, Sulloway 1979, Breger 2000, Roudinesco 2016, Phillips 2014, Whitebook 2017), nor does Freud himself in any of his letters or publications.

Her lifelong adoration of Sigmund is however very well documented. He was the favourite of her seven children. She called him 'my golden Sigi' and held the unwavering belief that he was marked for success.[1] She used to relish in chance incidents from his early years that she took to confirm her high hopes for him: when someone in a pastry shop exclaimed to her "You're a lucky mother! Some day the whole world will talk about this little fellow,"[2], or that once in a restaurant a busker-poet came to the family's table and declared that little Sigmund would one day be a cabinet minister[3].

Amalie's relationship with her favourite son did not become any less close in the years when he put forward his controversial claims about infantile sexuality and the universality of the Oedipus complex. Some of his closest psychoanalytic colleagues would pay their respects to her whenever they visited, and she would regale them with stories full of praise for him.[4]

Freud's highly personal letters to his intimate friend and confidant Wilhelm Fliess show that during his self-analysis he would occasionally approach his mother asking her to confirm such-and-such a childhood memory of his. He does not mention doing so with memories of an especially Oedipal nature, such as his recollection of seeing her naked during an overnight train journey, which he mentions in relation to his first known comment on the universality of the Oedipus complex.[5]

Given the meme this question is inspired by (and the comments under it), I can't help but suspect that this question may be partly based on a misunderstanding about what Freud's theories really were. Contrary to a popular misconception, at no point did Freud theorise that children wish to have sex with their mothers. His concept of sexuality is extremely broad, and genital intercourse may be the least significant aspect of it[6]. Moreover, he theorised that children are not born with any pre-given understanding of sexual intercourse and have no clear understanding of it until the Oedipal drama is almost over.[7]

Freud's mother was... a mother. Having raised six children, she was unlikely to have been particularly surprised by Freud's easily observable claim that little children undergo periods of passionate attachment towards their primary caregivers, that bodily satisfactions and losses of satisfaction become caught up in those early relationships, that they struggle with intense feelings of love, rage, jealousy and anxiety, and that all of this has consequences for the formation of a mind.

[1]: See for instance: Breger, L. 2000. Freud: Darkness in the Midst of Vision; Gay, P. 1988. Freud: A Life for our Time

[2] Anna Freud Bernays. 1940. 'My Brother, Sigmund Freud', in Ruitenbeek, H (ed). 1973. Freud as We Knew Him

[3] Freud, S. 1900. The Interpretation of Dreams. Standard Edition, Vol. IV.

[4] Bernays, J. H. 1956. 'Freud's Mother and Father'. In Ruitenbeek 1973.

[5] Bonaparte, A. Freud and Kris (eds). The Origins of Psychoanalysis: Letters to Wilhelm Fliess, Drafts and Notes: 1887 - 1902.

[6] Freud, S. 1905. Three Essays on the Theory of Sexuality. Standard Edition, Vol. VII

[7] Freud, S. 1908. 'On the Sexual Theories of Children.' Standard Edition, Vol. IX