Ultimately, your children are and should be your number one priority.

You and the ex get along. That's wonderful! It creates a healthy, loving, secure environment for your children and by extension you and the extended family.

This isn't a situation where you're still in love with your ex and want to get back together. Your romantic relationship is done and know you're concentrating on giving your children their best life.

New girlfriend is insecure/jealous. This will translate to many areas. If you were to have a child together -- would she become upset by your involvement with your other children? She would probably want herself and your child together to be the priority.

For me, given what you've said, red flags.

Your ex and new girlfriend don't need to be best friends but it would be ideal for them to coexist peacefully without competition.

Long term, I don't think you're new relationship will last.