It doesn't matter if a historian is a right- or left-wing one. Only if the sources he or she cites are verifiable and credible.

Radzinsky's quote fails the first prong of this test.

In Radzinsky's bio of Stalin he refers to what was allegedly told by Nikolay Kipshidze who was both Stalin's and his mother's doctor. The story was allegedly told to him by the mother himself.

The problem is that Radzinsky doesn't cite any verifiable source for this alleged claim by Kipshidze. There's not even a hint where this comes from.

His reference is therefore absolutely useless and cannot be used.

One part of the phrase is however directly corroborated by Stalin's daughter Svetlana Alliluyeva in her 20 letters to a friend:

http://www.lib.ru/MEMUARY/ALLILUEWA/letters.txt

Она была очень набожна и мечтала о том, чтобы ее сын стал священником. Она осталась религиозной до последних своих дней и, когда отец навестил ее, незадолго до ее смерти, сказала ему: "А жаль, что ты так и не стал священником"... Он повторял эти ее слова с восхищением; ему нравилось ее пренебрежение к тому, чего он достиг -- к земной славе, к суете...

She was very devout and dreamed of her son becoming a priest. She remained religious until her last days and when father visited her shortly before her death, she said to him, "It's a pity you never became a priest". He repeated these words with admiration; he liked her disregard for what he had achieved - earthly glory, vanity...

And somewhat indirectly by Trotsky in his Stalin:

https://www.marxists.org/russkij/trotsky/1940/stalin_v1/02.htm

В 1930 году, когда ей был уже 71 год, Екатерина, жившая в то время в Тифлисе, в бывшем дворце наместника, в скромной квартире одного из служащих, отвечала через переводчика на вопросы журналистов: "Coco (Иосиф) всегда был хорошим мальчиком... Мне никогда не приходилось наказывать его. Он усердно учился, всегда читал или беседовал, пытаясь понять всякую вещь... Coco был моим единственным сыном. Конечно, я дорожила им... Его отец Виссарион хотел сделать из Coco хорошего сапожника. Но его отец умер, когда Coco было одиннадцать лет... Я не хотела, чтоб он был сапожником. Я хотела одного, чтоб он стал священником".

In 1930, when she was 71 years old, Catherine, who lived in Tiflis, the former palace of the viceroy, in a modest apartment of one of the employees, responded through an interpreter to journalists' questions: "Soso (Joseph) has always been a good boy... I never had to punish him. He studied hard, always read or had a conversation, trying to understand things... Soso was my only son. Of course, I cherished them... His father Vissarion wanted to make Soso a good shoemaker. But his father died when Soso was eleven years old... I didn't want him to be a shoemaker. I wanted one thing to make him a priest."

The main part remains uncorroborated.

However, I found Radzinsky's source, despite him not citing it. It's Leonid Spirin's article "'Живите десять тысяч лет.' Письма Сталина к матери" ("'Live ten thousand years.' Stalin's letters to his mother") in Nezavisimaya gazeta, 13.08.1992 (154 (325)), p. 5, which is available here: https://m.yeltsin.ru/press/newspaper/detail6423/

I saved the key part here: http://web.archive.org/web/20191106174631/https://i.ibb.co/375Ry5s/ngstalin.png

Spirin was apparently a professional historian, unlike Radzinsky, who is more of a "popular" one, if you get what I mean.

So what was Spirin's source? He says that it's an unpublished memoir of Kipshidze from some Georgian archive. Unfortunately he doesn't even name the archive.

The same principle applies as to Radzinsky, the quote is not verified, though at the very least Spirin specifies that it was from a written memoir from some archive. It is thus quite possible that the quote is authentic - though this authentic quote could itself be hearsay.

It should be noted however, that Spirin doesn't ascribe this story to Stalin's mother. Rather, it was allegedly a part of a прилюдный разговор (a talk during which other people were present, a public talk). It thus could be that Kipshidze was present; or it could still be hearsay.

Of some interest may be the continuation of the story from the same source, which shows the whole conversation in a somewhat different light:

- Почему ты так мечтала о том, чтобы я стал священником? - спросил Сталин.

- Потому, - ответила мать, - что видела, как они мало работают и как хорошо живут. Почет у них также был большой. Вот я и думала, что лучшего занятия для человека нет, да и сама гордилась бы, что я мать священника. Но признаюсь, и в этом я ошиблась.

- Why did you dream so much of me becoming a priest? - Stalin asked.

- Because, - said the mother, - I saw how little they worked and how well they lived. They were also greatly respected. So I thought that there was no better occupation for a man, and I would have been proud that I was a priest's mother. But I confess, even about that I was wrong.