We had the same situation. My sister-in-law would bring her little yappy dog and her full-sized labradoodle every week. It was a disaster. We finally talked to my wife's parents, they talked to my sister-in-law, and now her dogs don't come (or they stay outside).

It's made the family dinners so much better, and I think it honestly made my FIL and MIL's life easier (the dogs were bugging them too, and our concerns made it easier for them to go to the offending people with a softer "We've been getting complaints...")

But, at the end of the day, the only thing you can really control is yourself. If you're conflict averse, consider just asking about the dogs the next few times you're invited over ("Will the dogs be there? They will? Ahhh, I don't know if we'll be able to make it"). They'll get the message.