You sound really lovely actually, so stop putting yourself down! 🌷
I could argue either way - helpful huh! 😂
So, just some random thoughts...
Your kids are at a good age now to get a family dog. If you leave it 'a few years' they'll be getting to an age where they have more evening activities, be getting to the age of going out with their friends more & generally not just 'hanging around' at home after school. A dog is a commitment for such a longtime. Once the kids are at uni/starting work age it's nice to have the freedom to reassess your life and maybe do things that weren't practical when you have children. Having a dog can be very 'tying' and you might not want that for quite a few more years.
What do your kids normally do after school? I presume they come home to you? Can't you not block out 30/45 mins to take the kids & the dog outside for a walk? I know all about working from home, but sometimes you just have to stop working and prioritise other things. It's too easy to let it take over.
If DH really wants a dog, why can't he get up 30/45/60 mins earlier & take the dog out for a run?
Puppy's are adorable but it's like having twins for quite a few weeks/months. DH would definitely need to share 'nights' and do a lot of other stuff so you could make up for not getting much done in the day. I think you would be better off getting a slightly older, but still young, dog.
Definitely spend time finding a breed/dog you love. Even us dog lovers have favourites (cocker spaniels/cocapoo's) and lesser favourites, no names mentioned greyhounds. You'll find one at the rescue who melts your heart. However, there's a balance here because you need to know what your DH would like. There's no point in coming home with a Chihuahua if he wants a Doberman. Not sure if the kids would mind what it was?
Mess - DH will need to step up with this as well. Dogs make a mess. Hair, muddy Paws, wet noses. Beautiful mess monsters. It's one thing that puts me off getting another one. It's so nice not having additional dog mess to deal with.
Move near me & Aunty Annie will dig sit, dog walk & offer a holiday home! 😊 Although I can't have a dog right now, I'd love a small share in one.