Is the mother obligated to financially assist her daughter to be fair, after she bought an apartment for her son's marriage, especially given that she has an additional sum of money?

The default is that gifts from parents to children should be equitable, based on the hadith (definition): "Be just among your children." Justice, in this context, includes giving according to the child's need. So, if a son needs assistance in purchasing housing for marriage, there is no harm in helping him. This is the view held by some scholars, such as Ahmad ibn Hanbal. However, if the son is self-sufficient, the preponderant view is the obligation to equalize the gift between him and his sister.