I’m suggesting this is easily resolvable. Splitting up yet another family because of a minor disagreement (yes it is minor and yes I do think people get to veto having people in their home even if another householder wants to allow it).
How we work, and most healthy normal functional people work, is they discuss, compromise and move on. They don’t break up families on a whim.
Disagreements are a normal part of relationships. You are not going to agree on everything 100% of the time.
In our household, how we resolve issues like this is we have a frank discussion about who’s needs or wants have greater weight and the weight of the affect each person’s need/want on the other person’s happiness in the situation.
For example, I want to paint the hallway green, husband wants it yellow. I really really dislike yellow, he prefers it but doesn’t hate green so we compromise because my option doesn’t make him unhappy, he’s ok with green but it’s not his favourite, but his option would make me unhappy.
In OP’s situation I would suggest she has the right to exclude the ex from her home because her right and happiness to feel safe and comfortable in her home outweighs both her DH’s and SC’s want to have an open door to ExW.
The reason for this conclusion is because having ExW in the house isn’t necessary, there is no need to have there at all. Calls, texts, FaceTime, email etc can all be used to communicate without her being physically present and will cause no harm to any of the householders.
The SCs have coped fine not having dad enter mum’s home, so they will be fine.
However, ExW entering the home will specifically cause emotional harm to OP (anxiety, not feeling safe etc) and therefore the logical resolution to this is for her husband to respect this and not want to cause unnecessary upset for his wife. His current wife’s needs should always outweigh his exWs. She is no longer the priority and other than having a general consideration for her overall well-being, he should not be invested in her.