If I stop doing child care for two years before selling my home, can I avoid paying taxes on my house depreciation?

No. You are referring to an old rule that expired years ago. Back then you could avoid paying taxes on the profit on the sale of your home if you were not in business for two out of the last five years before you sold it. That rule is gone. It has always been the case that you will have to pay taxes on any depreciation your claimed on your home (or were entitled to claim) regardless of when you sell your home.