It's not resilience you need. It's for him to take responsibility.
It's not your responsibility to 'help him' move forward. It's your responsibility to protect yourself and its his responsibility to put boundaries in place and both of your responsibilities to present a united front.
If your mental health is suffering, this situation is not tenable in the long term is it?
This is what I would do.
Write down the main and salient points. Write down how it makes you feel. Read it through and take out any emotion from it. Keep it to facts.
Your ex does A; you respond by B; it makes me feel C. Factual. Read it and reread it. Just to he sure its exactly what you want to say and exactly what bothers you and why.
Then I would tell him you want to have a proper conversation about the situation about his ex. Tell him it needs to be factual and that you both know what the emotions involved are But that's not what this conversation is about.
Explain it to him as you have written it. If you find yourself ad libbing and putting in emotion. Stop. Apologise and then get back to the facts. If you stay calm, there is less for him to react to. Don't say, "It's affecting my MH," tell him what it makes you think and describe how it makes you feel - eg I feel anxious when this happens because... don't criticise or point fingers.
If he becomes emotional - tries shutting it down, gets upset, agitated, angry whatever. Remind him that this is an unemotional conversation and that you want both of you to discuss it to find a solution that works for you both. Not his ex. She is irrelevant in your lives. She is only able to cause problems between you or in your home because you are/he is letting her.
If he refuses to engage on a calm level; can't or won't regulate and manage his own emotions then you have a different problem and I would seriously reconsider the relationship.