King Charles Cavalier spaniels have such endemic health issues that unless you really know the breeder, then that is an idea I would never recommend. The risk of getting a dog with brain or expensive terminal issues later when you and your children are really attached to the dog would be too high.
A gundog, per se, of whatever breed would be great with your lifestyle and children.
Except for labs who are designed to eat and eat and eat some more. If you aren't going to exercise much, I predict you'd end up with a very fat role poly one which would be cruel to the dog.
A dog is like a teenager and comes to expect a certain routine as the benchmark standard. That is, if walked for three hours, they expect 3 hrs every day. Ditto meals, so if the "30 mins" is off lead and stimulating (had the battle is wearing out their minds by walking in different places each day so they don't go onto plodding auto pilot) then your plan is fine.
Except don't get a husky anything, despite how cute they may be - the most muzzled, bad tempered and miserable dogs i regularly encounter walking my setters are husky breeds who the owners coop them up all day while they're out at work and then the owners wonder why they cannot let them off lead or why they attack other dogs.
They, like dalmatians, are designed to run and run and run.
Rescue greyhounds run for very short periods and then crash out all day. They'd be great, but perhaps not cuddly or as affectionate as a spaniel or a pointer would be.
Hounds run off and have no recall and are more food orientated and eat poo so I don't think, reading between the lines of your lifestyle, that they'd be suitable either.
You will find that a pure bred KC registered dog from a proper KC approved breeder will be "only" £750-800. These cross breed something-poos or trendy types will be four figures for a dog that really has no traceable health line. And that is risky and upsetting in the long run.
I expect to be flamed about Cavs, but hey, google to or ask the Animal Health Trust for their opinion on the inherent conditions in the breed.