The work that stay-at-home mothers perform is labor.

Unfortunately, it unpaid labor. There are no benefits. There is no pay. There is no time off. Not only is it a few steps away from indentured servitude, you don't even gain any marketable skills from it.

Therefore, SAHMs should unionize.

Striking would be as simple as leaving their house to stay somewhere else until they receive some form of compensation. Either their partners can fork over money, their partners can figure out being a single working dad, or the government can start providing benefits to these women for the work they do in raising the next generation (which, you know, is actually necessary for society to continue functioning on a long-term scale).