OP, as a SIL to an addict, I reiterate what some of the other PPs have said: Do not invite your MIL to your home. She will bring your BIL, because she will not respect your boundaries. Enablers are all about appeasing the addict, and expecting others to "be the bigger person."
When DH & I moved into our first house, SiL would pitch fits every time we invited FIL and MIL, as DH made it very clear to all three that SIL was not welcome. To placate SIL, MIL would stay home, leaving FIL to come by himself. MIL died two years after we married, without ever seeing, much less setting foot in, our home. MIL was such an expert enabler that it wasn't until after MIL died that he even realized that SIL was an addict and had been forging checks on their joint account to pay for her habit. Poor man died five months later with an empty bank account.
That is really
Having had a sister who was an alcoholic in denial until the day she died, I had a period of not seeing my sister for 7 years. Sure, I heard about her, but she stayed away from me. She knew I would not enable her. My kids never met her until the oldest was almost 5. My take on it was that I would not want her around my kids if she was any random person off the street, and because she was family, it didn't automatically negate that viewpoint. In fact, because she was family, I expected her to set a better
example for my kids than any random person off the street. She couldn't do that, so I had no desire to be around that behavior (disease), or let my kids be around it, until such a time as she could show me that she was done blaming others for everything and was ready to take responsibility for herself. Unfortunately, that never happened.
But we were never close to begin with, so perhaps it was easier for me to take this stand, because it was actually a relief to not have to worry about her. OP, Kudos to your DH for being able to (mostly) stand strong about keeping his brother away from your kids. I'm sure he had some sort of a more brotherly relationship
once, so this must be hard for him. I can even kind of see why he went to the birthday dinner; his brother has probably ruined a lot of times/memories/events, and your DH didn't want him to fully ruin his birthday, so he went anyway.
But I do now kind of agree with a PP who said that MIL needs a consequence for foisting BIL on you during your DH's birthday dinner. And she should know about it (otherwise it's not a consequence). (said by your DH) "Mom, we were going to invite you to our house on Saturday for our big dinner, but we decided against it because of what you did for my birthday dinner. When it came right down to it, we knew we couldn't trust you not to bring BIL on Saturday, so we had to make the tough decsion to leave you out of our celebration. We know you don't feel the same way about him as we do, and that's your right. But we also have the right to our feelings on the subject, and if you can't respect our feelings, then we can't spend time with you."
That's perhaps a bit blunt, but I'm sure you get the gist of it. OP, good luck, and next week, give thanks for holding your ground and maintaining your peace and safety by keeping BIL away.