I’m a dog owner. Have been fur over 35 years (various dogs). We don’t assume we can take a dog everywhere. We ask.
we sometimes book into a dog sitter (do not like kennels as our dogs are pampered. They’d be scarred in kennels), we can leave our dog home for a few hours alone or we take with us.
any time there is possibility of fire works, we take our dog or have dog sitter. None of our dogs (thankfully) have been reactive, but you never know.
we have a dog flap and a secure garden so they can go out if they need to “go potty”. They’re also confined within the house in a large room.
however, we do try to go to dog friendly restaurants, cafes and pubs. Our dogs were all very socialised and would happily sit under a table. Often, people never knew there was a dog until we got up to leave. We also bring a bone so the dog is happily chewing away and entertained.
we do ask if invited out where we will be gone for more than 4 hours (including travel time). Our dogs were all ok to be alone for that duration.
in people’s homes that don’t have dogs, we’d keep our dog in lead, bring a bone and dog bed. We’d keep the dog right next to us. A long walk before we get there and a few short walks while we’re at someone’s house keeps the dog entertained and tired. These walks on pavement so they’re not wet nor muddy. Wipe paws so no paw prints in house.
this may not be possible with a rescue if it has been traumatised, have separation anxiety and may not be possible with puppies who have not yet been trained.
you’re not unreasonable to not want dogs in your home. You shouldn’t have to defend why/why not.
you could , however, ask for your family members to control their dogs’ behaviour as described above. That is not unreasonable and would mean compromise by all parties so everyone could enjoy Christmas together and stress free. If they can’t control their dogs, then of course they should not be bringing to your home for Christmas.