It’s a bit of a complicated situation but I believe there is a proper setup that can work for something like this. You both need to talk properly about what arrangement would truly be best for the children’s well-being.
When children are involved, it’s no longer just about whether you are happy or not, what matters most is that the children are in a stable and healthy environment.
Maybe he still loves you, which is why even though he feels something is missing or he’s not fully happy, he still hasn’t left your home. Always remember that communication is the key to solving any problem or misunderstanding.
As for the part where you feel uncomfortable with his ex’s involvement, like she seems to still act like a stepmother to his children, it’s important that you also tell your partner how you feel. Let him know that you are not comfortable with that kind of setup, especially with people coming in and out of your home freely, as it can feel like a lack of respect for you as his current partner.
Whatever decision you make, always consider what is best for the children.