I would like to know if my ex (we were never married) can prevent me from bringing our children around my new boyfriend.

Unless your custody agreement specifically prohibits you from having your children around your (not so new anymore) boyfriend, or he's a substance abuser, abusive or a criminal, their father absolutely cannot prevent you from having the kids around him. It's not clear to me how he'd even prevent it, given that you have joint custody. If your ex is withholding the children from you on your days because of your boyfriend, you need to take him to family court for violation of your custody agreement. Don't wait too long- don't let him start to poison your kids against your boyfriend, because I guarantee you he's already started to try to poison them against BOTH of you. Lay down the law with your kids' father, and if your ex won't follow it, take him to court.