We travel with 4 Dachshunds, it's not always easy. We don't have breed issues, but often quantity. Have to look at their pet policy online and hold them to it. If they don't have a limit and I make a online reservation, I hold them to it.
Three can be just as tough I'm sure. You have a Lab mix, leave it at that! Might be harder though if it looks more like a Pit...but if it doesn't, it's just a Lab mix.
We always try to be honestly creative. I go into check-in wearing the doggie bag holder on my belt and make a point of showing it to them and that I never go anywhere without it. I guarantee them there won't be a problem. I haven't had to use it yet, but I'm prepared to tell them I have two dogs, and the woman I am traveling with (my wife) has two dogs. Their policy isn't clear whether it's two pets per camper (person) or camper (rig).