You really don’t say what the problem behaviours are, so I assume you just want sympathy and be reassured it is ok to want the dog out rather than solving the issues.
You just say that he eats the cats’ food (not really an issue putting the food out of the reach of the dog, really) he dribbles , he refuses walking some times, and you clean the mess. But you don’t say what kind of mess (hair? Poo? Pieces of your sofa?), I assume he is dribbling saliva, not wee, which is something some breeds do and, as for the walking, if you are not walking it for ten miles in full sun that dog might be in pain, is he one of those breeds prone to hip, knee or respiratory problems?
I believe the bottom line is that you don’t like the dog but that dog has some special meaning to your partner, much as your cats have a meaning to you, so the catch 22 is that you are not going to be happy with the dog there but he might resent you and your cats forever if you force him to give away the dog. So the question is, what do you prefer in the long run, putting up with a pesky dog or a resentful partner?
The second question is, have you got your home together or either of you moved into the other’s? Just asking this as it wouldn’t be the first time that someone will be asked to move out if they don’t like the pet.