It's great your mindful of getting from a good breeder, but I'm going to be the party pooper here; a good breeder will not sell to you in even 2 years with children that young, regardles sof whether your child is at school or not.
Lots of good breeders are becoming increasingly wary about selling dogs to families with young children because even if someone is home alone all day that doesn't stop the main issue; children harassing/bothering the dog and parents not acting quickly enough to prevent disaster. If a rescue won't give you a dog because your kids are too young, chances are a good breeder won't either. And obviously not getting from a good breeder opens up a whole can of worms...
Most of my local breed club have 8 as the minimum age, many are moving towards 10 (which I what I, personally, consider appropriate) given how many bites and attacks happen on children in family homes.
Nearly 70% of all dog attacks happen in the family home and nearly 80% of bites on children are from dogs they know. Why? Because children and dogs do not mix.
But, if you do want to plow ahead...
Labs are great dogs. 'Red fox' is just what the puppy farmers call it though to drive sales and sell defective dogs based on their colour (like 'sable' Cocker Spaniels a few years ago). 'Red Fox' falls under 'yellow' in terms of breed standard. More importantly those darker labs are usually for 'working' lines which is a very very different dog to the labs you are imagining. The working line labs I know are more akin to GSDs in term of drive and intellect than they are to show line labs. Not really suitable for families with your children or novice owners - if you don't work them, they'll work you.
Cockers are lovely, but they are incredibly sensitive. They're prone to a lot of behavioural issues if from a poor breeder (back to my point above) and given their sensitivity can be challenging with young children. Some idiot will come along in a moment and say 'oh cocker rage.' 'Cocker rage' is what bad owners call bog-standard behavioural issue. Chances are if someone is saying their cocker has rage, they're just an incompetent idiot who shouldn't have a goldfish let alone a dog. All behavioural issues have some sort of trigger and cockers are prone to lots because they are sensitive and require gentle handling.
It's not just about size when buying a dog. It's about temperament as well. Some of the best known 'family' friendly breeds aren't necessarily the 'best' ones to have with young kids.
With all dog breeds, but particularly those prone to joint issues, you shouldn't be running it until it's fully developed. For cockers that will be about 2 years old, for labs closer to 3. Doing so can cause life-long, life-limiting joint conditions that will be entirely your fault.
And not leaving a dog alone for a few hours is fine. But what about a puppy? Realistically you cannot leave them for more than a few minutes at a time for the first few weeks and you have to build it up gradually. If you were to get a cocker and you were leaving it for a few hours at a time from a few months old, it's probably only going to end up one way; with separation anxiety.
I also disagree about involving children in training. Young children and training dogs do not mix. Children do not have the necessary motivation, body language and 'tone' to train a puppy. You can involve them as much as you want, but chances are they'll probably undo the good work you've put in by turning it into some sort of game and exciting your puppy. And if you want a high-energy breed, your dog needs to be trained well. Neither of my DDs have been involved in any of the training of my dogs, except my youngest (but DDs now much much older), and yet all my dogs listen to them and have for years. Why? Because I trained my dogs well.
The best training class is one you don't attend. Most of them involve sitting around for 45 minutes and actually only doing things for 15 minutes (at max). It's a bad environment for a puppy as it's overstimulating and your puppy gets to see other dogs ignoring their owners commands. Better to do 1-2-1 training with a professional (or indeed if you know what you're doing, do it yourself) to avoid those situations. It's also a big cause of dogs learning bad behaviours and can cause early nervousness issues (lots of manic puppies in an enclosed space is just a bad idea).
If you do really want a dog, please consider a poodle. I love labs and cockers. I consider labs great for people with kids, but just not kids that young. And given good breeders will have wait lists, can afford to be fussy, and will likely swerve you with two children so young, you're going to end up buying from someone who is not a good breeder and will thus not breed robust, healthy, dogs, and as a result everything will be much harder than it needs to be 😊