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A true friend wouldn't turn on you for dating their brother and wanting a relationship without the family being involved and if she did indeed turn on you then she really wasn't a friend and you should verbalize that to her. I think you should follow your heart and keep your relationship private aside from his family but you need to also talk to the friend and tell her it's unfair how she is treating you after you have been friends for so long and that she should know you better than that. It's unfair for them to interfere in your relationship since you are both adults and can very well handle your own relationship. Everyone is entitled to their own opinion but they should keep it to themselves and your boyfriend should tell them that, he is 40 years old and doesn't owe them any explanation about your relationship and where it's going.
I would call him and apologize and be honest about how his family pressured you and pushed you to break up with him, tell him that you care about him and want him to be with you no matter how his family feels about it. Tell him you want to see where the relationship can go. Life is too short to live it according to how everyone else wants you to live it or else you would be miserable and alone. I would carry on the relationship where it left off and not worry about what other say. If you have anything to add please just click the reply button.
Take the relationship slower so that you both can work out the issues at hand but his sister cannot expect him to be alone and lonely just because the mother of his children and him cannot get along that isn't very fair. It's not like the two of you have to rush the relationship maybe if you gave them time to adjust and see that you are indeed encouraging him to see his children then they may be more accepting of the relationship. The first thing you should do is talk to the ex and ask him to try again, second thing you do is set some ground rules as to how much the family knows about the relationship and what goes on in it, thirdly do not mention your relationship to his children it may be too much for them to handle right now give it some time for it to sink in that their mother and father will no longer be together and it's best for everyone involved, fourth talk to the friend and tell her to please just give you a chance and if it harms the children in any way you will step back and give him time.
Also allow him to be there for his children no matter what even if you had something planned and something comes up with the children as long as it doesn't happen too often then allow him to be there whenever they need him then they will see that you are not a threat and aren't trying to take their father from them. Sometimes children act more mature than adults do and the child may surprise you and take to you very easily if they can see that you are with them not against them, if they get even the littlest hint that you are a threat they will turn on you and never give you a chance. Also you have to decide if you are truly ready to take this on with everything that has already happened is this too much too soon?