Relationship advice needed

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hi let me get you up to speed. i have been in a relationship for near on 15 years now. at first it was great then over the last few years its not so good. for 11 of these years we lived together under the same roof, until i moved out for reasons that i disagreed with what he was doing, which was illegal. i have two children to this man, and now that i have my own place he comes over to stay on the weekends to spend time with me and the kids. i have told him that i want to end it, all because he has been listening to people who i felt were my friends. these so called friends have been telling him that i have slept with other guys while we were still living together. this is slowly getting worst. it doesn't matter that i have repeatly told him that i have not slept with anyone but him over the time we have been together. he just wants to believe what everyone is telling him. i know you don't know me but its not in my nature to slept around, after all im nearly forty and have only had 6 boyfriends. the main problem is that everyone is telling him that Tay who is 4 now, is not his. i know he thinks this way too, because she doesn't look like him unlike our son. so i told him that he should get a dna test done on both of the kids. my problem is i don't know if i should stay in this situation and do i make him understand that he is listening to people that want us to spilt. OR do i end it totally as he doesn't beleive me over them anyway. if you can help me with some advice on how to handle this situation i would really be greatful.