What to do when you're ex doesnt want you to be with anyone else?

I have a 3 year old and a 6 month old with my ex. We broke up several months ago for a number of reasons including his temper, abusive behavior, and cheating. He continues to call me names and threaten me. I have been seeing a wonderful guy for a couple of months now and we typically just go out for a couple drinks out of respect for my ex not wanting my kids around anyone. We are now at the point though where we have decided to be exclusive and would like to spend more time together meaning he would end up being around my kids. My ex doesnt really see the kids too much and has a new girlfriend as well who said they would like to spend time with the kids which I am fine with. How do other people deal with their ex not wanting their current boyfriend around the kids? He threatens me as well as my boyfriend and has let me know that if he ever finds that he has been around my kids he will physically injure me. Would you go ahead with moving forward or should I stop seeing the new guy?

Thanks for the advice. I absolutely know that if he does anything I should call the police. I did have a restraining order and he's only supposed to have supervised visits with the kids but I'm not at all concerned about him hurting either of them. I just feel like I took the first step to say yes I understand you are seeing someone else and I am ok with her meeting the kids and all I got from him was threats regarding my boyfriend being around them. I just want to make sure I'm not sounding completely unreasonable because obviously I'm not seeing it from his side. With my kids being so young, there's really no concern with the kids having an issue with it and my new boyfriend has a 2 year old as well so he understands what is required. His mother has custody of his child while he's in school but he sees him pretty much daily. It's a little early to say that he's the one but there's definitely a possibility so I'm just trying not to make the situation worse.

damn. if he hurts you at all, you should contact authority! and if his new girlfriend gets to spend time with your children, why shouldn't your new guy? follow your heart... but be careful. and if he does injure you, then you shouldn't let him get away with it.

I'd advise you to get some legal aid and a restraining order. I would stop his visitation with the kids. If he has a bad temper and is abusive to you, he may exhibit the same behavior toward the kids.