Hi @Swanny and Gator, and welcome to the site!!!
As you're about to find out we love to see pics on this site! So can't wait to see Gator!!!!
Our newest addition, Daddy, also has a corkscrew tail so I know EXACTLY what you mean. We use the sensitive baby wipes too, because they are good for wiping out the wrinkles daily. I just kinda either sandwich him between my legs with his head behind so I can get to his behind or I squeeze him into a corner. He always gets baby carrots, frozen green beans, frozen blueberries or a chunk of cucumber as a treat so he has learnt that if he "takes one for the team" so to speak ... then he's going to get something yummy at the end of it. One thing I have learnt is that bulldogs love their food SO much that you can more-or-less bribe them to do anything if you've got something edible in your hand!!
As for the alpha-demeanor ... well you don't say how long you've had Gator but you obviously got him when he was an older dog so I'm sure he is trying to work out where he is in the hierarchy. So right now I expect he's pushing the boundaries to see how far he can go. You say you have three kids, well I'm sure that they are going to test to see what the limits are if they haven't done already. So just imagine Gator as your teenage son who is just trying to see how much he can get away with before he loses the cell phone!!! You wouldn't be skittish in front of your son or back down because then who would the parent be ... you or him. It's the same with Gator.... you are the boss and you have to tell your fur-kid that he does as he's told or there will be trouble!!!