The best thing to do in a situation like this, is to have a serious, mature conversation with your family. Invite your boyfriend over or invite your family out to dinner with you, and then bring your boyfriend along or have him meet you there. When you sit them down, you can both tell them how much you love and care for one another, and how you know that things have been rocky in the past, but you both are working through them because the relationship means a lot to you. They need to see that you are adults, and that you are capable of making your own choices. It is also important to have your boyfriend speak up. He needs to tell them that he is extremely apologetic to you for the pain he caused, but he loves you very much and is thankful that you are back in his life. By taking this initiative, you are showing them that you respect their concerns about you, but you are old enough, responsible enough, and intellectual enough to have an adult relationship with your boyfriend. As adults themselves, they will come to see your point of view, because with their own life experiences they surely understand that relationships are tough, and sometimes people get confused, make mistakes, and etc. I guarantee that if you use this technique, you will gain the respect and approval of your doubting family members.
Thank you in advance, and please remember to press the accept button if you are happy with your answer. :-) Good luck with everything!
I believe that if you have spoken to him, voiced your concerns, and you feel that he is genuinely apologetic ready to change, give you what you need, and that you can trust him, then yes, I think you are making the right choice by taking him back. There is nothing wrong with giving someone a second chance. We all make mistakes. :-)
If your boyfriend cannot be there then you will have to sit down with your family yourself. Communicating with them in the right way is still the best way to resolve this issue. Tell them exactly what you told me. Tell them nicely that this is the man you love, and if they love you they need to learn respect your decision to continue the relationship and to accept him as a person. Tell them that it is important to you not to drive a wedge in your relationship with them because of him, and that is why you are having this conversation.
Good luck and I hope it works out well for you. :-)