I'm sorry you are struggling though.
It doesn't sound complicated to me. Complicated to FEEL maybe, but not complicated BEHAVIOR.
You want to have the ex-wife as GF/lover and cohabitate so all the children live under one roof. Your DH and his ex-wife go along with this and try it on. Now you feel struggle because you now know DH is not really into her as is doing it "for you", and you know she is into him and because you care about her, probably don't want her being used/strung along.
So how do you restore right relationship within yourself, with DH, and with her?
can this eventually cause issues where I will have to end things with her because of his not really wanting to be with her with a close relationship like he and I have?
You already have issues. Otherwise why post?
Could ASK them both where they stand rather than wait for things to explode from tension or whatever.
Could ask DH to confirm that he prefers to STOP having sex with the ex-wife. Could tell him you are ok with it, and you are ok dealing with whatever happens next once he ends it. He doesn't have to put out and have sex with her for your sake. Is he ok if you continue to date her? Continue to cohabitate? Could get answers.
Could also ask your GF (his ex wife) if their side of the triad breaking up means she also wants to break up with you. If that means she wants to stop living together. Ask her if she's aware you want to continue to date other people and not be exclusive. Could get answers.
Could ask you what YOU want? Maybe you want to date her but NOT cohabitate but live nearby?
You could lean into it
and resolve it rather than shy away from it from fear of potential conflict. You seem to be avoiding it because you don't want to feel anything yucky once it is out in the open. And in being avoidy... things could just escalate.
You could think about changing your conflict resolution method
from "avoid" to something else. It's being felt now -- at least by you and DH. She seems to know he's not all that into her. So... you tried it on and found it's not working for ALL parties.