Honest answer? They don't - particularly if you get a puppy.
People usually take several weeks off to bed in a new puppy and then months to get them used to being alone etc. So, you'd have no choice but to take your dog to daycare, but most daycares have an age restriction (i.e. dogs have to be a certain age to be allowed in) so you can't rely on that straight away anyway. This is because lots of dogs - even very stable adults - do not like puppies, so having puppies in the same daycare setting as adults dogs can be dangerous. If they do allow puppies, chances are they are the sort of place you wouldn't want to leave your dog anyway. It's not even the two days a week you're both out. It's the weekends - you can't swan off to take the kids to activities or friends houses, and leave the puppy alone.
Yes, you could get a rescue - but lots of rescues don't sell if you have a young child. And, of course, you have the 3 month rule which means it can take three months (minimum) for a rescue dog to settle in.
I mean, you could do it - and you could leave the puppy alone two days a week - but you'd be a pretty rubbish owner and you'd probably end up with a dog with some quite serious behavioural issues.
People will pop up and tell you every breed under the sun would suit your family life. And they'll tell you they left their puppy alone from day 1 and it was fine - they are not the norm, and they have taken a huge risk in not only their puppies happiness, but also it's safety (given puppies can cause serious injury to themselves in only a few moments unattended).
But, in your circumstances, a good breeder would not sell to you (not simply because of your lifestyle, but the age of your children) - which, if you do proceed, means you're far more likely to end up with dogs with severe behavioural issues/defects and severe health issues/defects.
If you really want a dog, I'd recommend you get one that's very placid and happy to be left alone - a rescue Greyhound etc. Don't try and get a spaniel or a retriever or a poodle because that will end in tears and probably a bite.