I vote with everyone else so far on the "not move in" part.
We (mate & I ) have kind of been in this situation and did otherwise. Although in our case there was absolutely no danger involved or opportunity for big drama, because we hadn't really had sufficient time to have some of the deep discussions necessary, it turned a beautiful friendship into something strained. Living full time with someone is a VERY different thing than dating or hanging out together.
We got through it pretty much but looking back wish we had maybe looked for a better alternative. Not that there probably was one - but we didn't even look - or discuss it. Just loaded up her stuff one night and home we went !
Your heart is in the right place it seems but try to take what time you can to have some deeper discussions and consider alternatives as part of that. Helping her (and children) without making things worse for anyone is the objective.
Good luck and keep us posted.