Praise be to Allah.
If the man gives his wife a certain amount of money to spend on the housekeeping, and she is able to manage it well and save some of this money to use in the future, then there is nothing wrong with this; rather she is to be thanked for doing it, but that is subject to certain conditions:
1. That this does not involve deceiving or lying to the husband, such as if she asks him for things that she does not need, then she does not buy them and saves that money instead, or she asks for more than she needs, then only buys part of it and saves the rest of the money. That comes under the heading of lying and deceit, and is not permissible.
2. That no constraint should be caused to the husband and children as a result of that saving, because the husband only gave her that money to spend on what the household needs.
3. That this saving should be in the interests of the family as a whole, not for her personal interests, or to spend it on things that the husband does not approve of.
4. The husband should not have any objection to her saving his money, because the money belongs to him and he is free to dispose of it as he wishes.
If these conditions are met, then there is nothing wrong with what she is doing; rather it comes under the heading of good management.
As for her savings from her own salary, there is nothing wrong with that, because the salary belongs to her and does not belong to the husband, and she may dispose of it however she wishes.
And Allah knows best.