Hello Brokenkitty ~ welcome
I can certainly understand why this is a problem for you. The boy you like should be able to see this too. He may not mind upsetting people, but, clearly, you would.
You currently get on well with your ex, but, as he still has feelings for you, that may go wrong, if you dated his cousin ~ or even if he discovered that you like him.
The thing is, he and the rest of the family are likely to find out, anyway, because his cousin doesn't mind them knowing.
In the circumstances, it might be best if you spoke to him about it first ~ before he hears it from others.
Once you have discussed the matter with him, it may become clearer to you what you should do about this.
If he is comfortable with it, then there shouldn't be a problem, and even if he isn't, but if you have been honest with him, he may, at least, be able to come to terms with it.
It might help, if you left it a while, before pursuing the new relationship. What do you think?
Good luck.