It's dog saliva that's considered unclean.
But if a dog licks you, you wash and can pray (in an area without dog saliva on it).
Mil has a very excitable Collie, who shakes in mad delight when we visit and spends his time paws in my lap staring soulfully into my eye (breathing awful stinky breath on my face), love him to bits. He stays downstairs so I'm free to pray upstairs and he doesn't slobber or try to lick anyone.
Fil has a massive chowchow with a penchant for having is bum scratched, I spend ages scratching his bum whilst he leans on me and makes weird happy noises. Again fil has a dog free space for where I can pray and the chowchow is not a lucky slobbery dog.
Culturally we grew up in a household with no pets, so some people who are Muslim are frightened/uncomfortable around pets. But I think so are a lot of non-Muslim people.
Just go about your day normally with all family members present including dog, & make sure if they're not comfortable about dog they have a dog free space i.e. Their bedroom.
No need to get terribly upset about it when they come in ask about the dog.
I've met ham eating alcohol drinking Muslims too. So I'd ask them that too.
My inlaws asked me about my dietary requirements. I love them to bits and would not dream of them or anyone emptying their house of food, drink and family pets. That's ridiculous.