myfriend, it is not ALL or NOTHING. Learning Torah is very important but you can still learn Torah and and a mother can still be at home. What you are talking about is ALL or NOTHING, which is two extremes.
You also ask what is more important for a mother to be at home or for a father to learn Torah. That is not a balanced question because as I said a mother can be at home while a father learns torah. Chinuch Bonim is a very important obligation for parents. We have learnt that there is a very big disadvantage to many children when the mothers are not at home to raise them. We have an enormous percent of children with learning disabilities, speech problems, at-risk issues, etc.
This also has not worked out so well for the Women who are expected to be Superwomen, Supermommies and Superwives. YOU can say all you want how important it is to learn Torah and it is, but that doesn’t mean that a man does not have any other obligation and that he can ignore ALL his other obligations and only concentrate on this one. A MAN has obligations to his wife, to his children, to his marriage and his family and he is not absolved of any of these obligations because of his choice. Even if his wife agrees to support him in his learning that still does not absolve him of his obligations! He is still obligated to show hakaros hatov, he is still obligated to take care of his wife and take care of his children. He still has to know when the agreement is working and when it is no longer viable.