New boyfriend shared custody of cat with ex. I’m I wrong to tell him to stop or leave me?

Anonymous
I’ll keep this brief. I met this guy on tinder 2 months ago. First date he told me he was previously engaged with ex girlfriend and they currently share custody of cat where he FaceTimes him once a week.

I ignored this and said ok. Then after 2 weeks he told me ex had miscarried twins two years go and that triggered the breakup. However a week later he then told me ex girlfriend found out he was seeing someone new and she was really angry. I was very confused.

Ex got so angry and she was texting him mean comments about me. She even hacked into his email to reset all of his social media accounts to find out my name. Anyways I was angry. She even went as far as adding me on all social media accounts and requested we have a call. I refused and told him to deal with his issue.

He dealt with it and told her he’s moving on and it’s not up to her to interfere in his life. Anyways, the cat is still an issue. It’s his cat, he bought it 2 years ago but the ex has been looking after him since the breakup.

He has told her he wants it back and she can see him once a month. This makes me so uncomfortable because I feel and have been told this is a way for both of them to still maintain contact after the breakup.

This hurts me because he has told his parents about me, organised a meeting with them soon, invited me to an important work event to meet his colleagues and introduced me to his friends. It feels like he’s doing the right things but this CAT and the ex are still in the picture.

It hurts so much because I’m trying so hard to be a great girlfriend and honestly it might seem to soon, but I feel so strongly that he could be the one. I don’t want to look stupid, but I refuse to have a boyfriend who is still entangled with his ex. Any advice? What would you do in my situation?
New boyfriend shared custody of cat with ex. I’m I wrong to tell him to stop or leave me?
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