Why didn't they just adopt?

Why? So you could miss out on the excellent movie? (not)

Because they were bat-poo crazy. They were also on the run for some other trouble. they had fake identities. Probably wouldn't have passed any background checks, even if they weren't on the run. She (accidentally) killed her last child.

I choose to believe what I was programmed to believe

She says to the kid "The ruler of the land wouldn't give Mama Bear a new cubby, even when she asked nice." I assume that means she applied to adopt and was rejected.

Because adopting isn't cheap. Plus I doubt these two were stable enough to pass background checks and stability checks.

they won't give a kid to a woman who just lost hers without some mental evaluation unlike you're buying a gun though.