Okay, here's my 2 cents, for what it's worth.
1st of all, I have been sick as a dog before and had doctors appointments (for myself) when I've had to take my kids with me. No one to watch them.
2nd - I have had plenty of vet appointments, most recently, with our EXTREMELY wild, rambuncsious puppy & both my kids with me, why couldn't they have taken the baby with them? Not that big of a deal.
3rd, I have never been to any doctor (mine or vet) where I have walked in and they say "Oh, we've been waiting for you, come on back" Nope, that doesn't happen, I guarantee they still had to wait 10 more minutes after they got there. They should Thank You, you probably cut 10 minutes off there wait time.
They need to get over it, save it for the "big stuff"!
There were two adults going to the vet, why on earth did you even have to come home from shopping? Sure its a hassle to bring kids to appointments, but we all have done it. I one time had to bring my infant with me for an emergency root canal. So a trip to the vet is no big deal. You really need to clear the air with your DH. He needs to know that you are his wife, first and foremost. Its commendable that he helps out his mother and brother, but at what cost to his wife and child? ANd for the MIL, I would absolutely say something to her. She can't be all that pissy if she's back at your house for a barbeque. You need to set some ground rules with her before she becomes any more dependent. Also, maybe have a little chat with the BIL.
