The obvious answer is that she's not really ready to reconcile with you. By stepping away she probably has come to appreciate your good qualities and there is a lot of uncertainty living on her own -- especially since her choice of affair partner may mean that work is unstable too. But, she's cake eating -- she also wants to take advantage of the freedom she's gotten.
You don't say how old your kids are, but I think you need to protect them. So I'd say, do NOT let her move back into the house, do NOT let your children see you two dating (it'll just get their hopes up), if you want to continue to date her you can (although you'll be told by others to simply let her go so you can move on), but at this point I think you need to move forward with the divorce.
You don't say how old your kids are, but I think you need to protect them. So I'd say, do NOT let her move back into the house, do NOT let your children see you two dating (it'll just get their hopes up), if you want to continue to date her you can (although you'll be told by others to simply let her go so you can move on), but at this point I think you need to move forward with the divorce.