No, you shouldn’t cut off the relationship. At 32, you have the right to make your own decisions. But I do think you need to walk in your family’s shoes a little. Love is driving their behavior. They’ve watched you make the same mistakes time and again. They are protective of you. They are protective of your kids. They don’t know your new guy the way you do. How do they know he isn’t the same type of “mistake” in another disguise? Six months isn’t very long to know each other before making the decision to make a life together. From their point of view, it may look like you are again acting on impulse.
I wish your family members were able to be kinder in expressing their concern but being angry at them for being concerned will only keep this going. Instead, think about how to help your family and your boyfriend get to know each other. This isn’t going to be accomplished with one awkward meeting. It will mean arranging for various people in your family to spend time with the two of you and your kids. Keep it light. Find ways to have fun, not confrontations. When they see that he’s a good man and that he’s good to you, chances are they will accept him.
I wish you well.