In some cases, yes -- you have to be employed in order to be eligible. You'd need to research them on a case-by-case basis. The same is true for EMBA programs; again, each school will have its own criteria.
Interestingly, UCLA Anderson's highly regarded FEMBA (Fully Employed MBA) states that they consider being a stay-at-home parent an acceptable form of employment. All such schools will offer career support.
Online MBAs offer less support and have fewer expectations of you as a member of their community, so that would be a very different option. Which is better for you depends on what you need from the overall MBA experience.

Good luck!