It really isn't your place to go giving your brother's phone number out to anyone. For your ex to ask for it is a bit inappropriate. I would ignore the request. If your brother had wanted this guy for a buddy, he could have made that happen a good while back. Then they would have each other's phone numbers. As it is, your ex doesn't need to be all up in your family's business.

After a divorce, I think it's appropriate for the former spouses to put a bit of distance between themselves and the families of their exes. It would be different if a strong friendship had already formed. That's not the case with your ex and your brother.

By the same token, you have no business texting your ex's brother wanting to get together for drinks. He was right to ignore your texts. Time to move on. You can't control how your ex talks about you or what his family believes about you. Let these people recede into your past where they belong. That gives you more of a fresh space to move on with your post-divorce life. With time, it will hurt less and less.

If they are good people, your family will take their cues from you. They won't encourage contact between your ex and themselves, if they see that it is hurtful to you. I can see where it would be. It would be alright to express to them that you need them to help you keep space between your current life and that of your ex. This would help you to heal.