Here is a Boston University article skimming over women's rights in the USSR from WWI to the 90s. Essentially, the USSR granted them rights to vote and divorce, but they had to take up jobs in factory and field. In addition to that, Russian culture is very macho, and men long refused to take part in any housework, whether that meant chores, fetching water, or even a bit of shopping. So Soviet women after the Revolution were now not only saddled with all the demands of maintaining a family and house but also with the same intensity of work their husbands were doing. Men were preferred to women in most jobs, and very few women served in higher government positions, which the article below claims confirms the USSR as a classic patriarchy.
This article comes off as a bit biased, but offers good basic information on the rights of working mothers and the increasing apathy of Soviet husbands, who could no longer take pride in being a breadwinner (as Soviet wages were kept low, meaning all couples had to work equally).
Anyone who has more information, please, speak.
Under Lenin, divorce was made much easier. Abortion was also legalised. This is because of a Marxist belief that marriage was a bourgeois institution, and that women were to be "freed from the bondage of children and family". This didn't last too long however, and the party (even under Lenin) soon came to question it's previous decisions. By the late 1930s, divorce rates in the Soviet Union were the highest in Europe at one divorce for every two marriages.
This led Stalin to embark on the "Great Retreat" whereby Stalin came to stress that the family was a stabilizing influence on society. Stalin reasoned that in order to be a good communist, one had to be a good citizen, and in order to become a good citizen, one had to be a good husband/father/wife/mother.
Industrialisation and collectivisation had caused large social unrest, and Stalin stressed good ol' family values as a remedy to this, attaching traditional values to women, such as their roles as home-makers and child-raisers. He also noticed that there were a great number of orphaned children living on the streets, formed into gangs. This further caused Stalin to recreate the importance of the family in the Soviet Union.
In June 1936, he reversed much of the social policy regarding women which had been written under Lenin, importantly:
Marriages now had to be registered to be recognised.
Divorce was once again made difficult
Abortion rights were restricted
The family was declared the "basis of Soviet society"
Homosexuality was made illegal
This put an end most of the progressiveness Soviet social policy may have once had.
Also, as birthrates were falling and many men were dying in the Second World War, in July 1944, the USSR introduced measures to re-affirm the values of the family, as well as to incentivise women to have more children. In actual fact, these measures restricted women's rights even further. As of July 1944:
Divorce was made even harder
Abortion was made totally illegal
Mothers with more than two children were declared "heroines of the revolution"
Parents with fewer than two children face heavier taxes
The right to inherit family property (restricted under Lenin) was re-established.
Though Soviet propaganda talked a lot about gender equality, in actual fact there was very little. In 1936, Stalin created a "Housewives' Movement" which was charged with "civilising the tastes" and improving the working conditions of women, but in actual fact the USSR was so rapt on it's war economy that the group received little attention or funding, a long with almost all women's organisations.
Some women gained income and status under Stalin, but these were rare cases, and almost always unmarried and childless women.
Women did become better represented in the workforce, largely due to a lack of men because of the war. in 1936, there were 9 million women in the industrial workforce of the USSR. By 1945, there were 15 million. In fact, by 1945, half of all Soviet Workers were female. In the Soviet armed forces themselves, over half a million women fought.
Despite women's massive contributions to the USSR and the Soviet war effort, equality was not really achieved. In real terms, women's pay fell between 1930 and 1945.
Sources
Lynch, Michael. Origins and developments of authoritarian and single-part states. Chapter 2: The USSR under Joseph Stalin London: Hodder Education, 2013, 54-55
Also my brilliant yet slightly wacky history teacher.
Here's a few related questions that have been discussed here:
Difference Between Womens Rights in Cold War Era Soviet Union and United States
(I hope it's acceptable to post these)
How gender-equal was their military really? I know of famous units like the 'Nacht Hexen' and the sniper girls, but was this more of a propaganda effort about how equal communism was, or were a lot of women making real contributions as fighters?
One big difference was actually in terms of consumer culture and how that affected women's lives socially and physically. Because Communist countries focused on heavy industry rather than consumer goods, not only were there few cars and telephones, but there were no tampons or pads. Also, there was not very much makeup, certainly not much good makeup.
I have a close friend from the Czech Republic whose mom grew up during Communism, and for her just these consumer goods were one of the big changes. For reference, Slavenka Drakulić also speaks about this change.
I'm sorry I only have sources from Czechoslovakia and Yugoslavia, but I imagine women in the Soviet Union had just as much a time finding these goods, and I haven't seen anyone else mention this angle.
I don't know much about the subject, but here is a free PDF version of the 1975 book Soviet Women by communist journalist and activist, William M. Mandel.
Just a little relevant-ish primary source here, making no inference either way.
"No party or revolution in the world has ever dreamed of striking so deep at the roots of the oppression and inequality of women as the Soviet, Bolshevik revolution is doing. Over here, in Soviet Russia, no trace is left of any inequality between men and women under the law. The Soviet power has eliminated all there was of the especially disgusting, base and hypocritical inequality in the laws on marriage and the family and inequality in respect of children."
Vladmir Lenin
https://www.marxists.org/archive/lenin/works/1921/mar/04.htm