Disbelief, I suggest that you get control of your money and your household stuff. She is not trustworthy right now. She also needs to understand her true income as a WAW, which will not include yours. She won't be able to find a place until she understands that. I've noticed in your last few posts she's made referances to "maybe we could rent later, if things work out...". DO NOT trust this. She is using these statements to get your money so she can purchase whatever she wants. Don't do it. Protect yourself financially because you and your children will need it.
My H stayed away from our kids too initially after we separated. It made him feel guilty and face the reality of what he'd done. I let them call his cell. If he didn't answer, they left him a message. I didn't even though I was close by sometimes for our youngest, I didn't say a word so he couldn't say I was manipulating her.
I would also suggest discussing a vistiation schedule next time she brings up moving. That way she knows you expect her to take some parental responsibility. If she expects to just runaway, you need to know so you can protect yourself legally.
Otherwise, you seem to be doing better at the validation and no pursuit. Hang in there. This isn't something we're naturally good at.