Making it a brunch won't keep alcohol away, sadly. Just yesterday BIL and his wife were pulling into the grocery store as I was leaving and BIL was in the passenger seat with a beer in his hands. It's out of hand. He was hungover all of mother's day. I'll just throw one birthday party, alcohol free. Anyone who is carrying alcohol will be turned away. Thanks everyone.

It's your party. No alcohol if you don't want that dynamic. It's their decision whether or not to attend, and THEY are responsible if they end up alienating themselves from you/DH/your child.

I don't allow smoking on my property so you MIL would need to go smoke at the stop sign if she wanted to. I'd say no alcohol too.

Do not do two separate parties to appease them. Say no alcohol. They're adults and they can decide if they want to come or not. Its your DD who will be hurt when she's older and realizes what a$$ they are, but she's 2 and she won't remember her bday party.