Do you think stay-at-home mothers will be happy?

Happy for a short time, but not for a long time. If nothing else, you will be very unfulfilled, and you will gradually lose contact with some of your former people. Although many of them are not friends, the circle has indeed become smaller, and the pressure of re-employment is great, and there is basically no advantage. Many positions will send you away as soon as there is a long gap.