We have 3 rescue dogs between 8 months and almost 8 years old. Both of us in full time work. I work remotely most of the time, occasionally have to go away (company based down South, we're in Scotland). DH works hybrid. DC are older now (teens) so they help. DM lives nearby and can help with dog sitting as well.
If you think you might need to go back to work and would be out of the house all day, you would at least need to find a dog walker who could come and walk them and break the day up. You may be able to find volunteers to do this on Borrow My Doggy, but in my experience you can't always rely on that and you need backup. Check if there's a local doggy daycare, dog sitter, or if you have family nearby, ask if they would be prepared to help when you go back to work.
If you can't afford dog walking/dog sitting services and have no family help, you can't afford to work full time and have a dog, it's that simple. Go on Borrow My Doggy as a borrower instead and walk/dog sit someone else's rather than having the responsibility and expense of your own dog.
With the ages of your younger kids being under 5, please, please do not get a puppy. Too many puppies are returned/end up in rescue because they are incompatible with young children/owners don't have time to train them properly/walk them enough. Animals should not be disposable, but sadly, most of our fosters and rescues have come from homes with young kids where the owners didn't think it through fully and then couldn't cope or the dog ended up with behavioural issues because they didn't train, unintentionally neglected the dog's needs, or in the case of our 8 m o rescue, stupidly allowed young children to roughhouse with the dog. None of these families were bad people or abusive owners, but their naivety, inexperience and lack of foresight led to their dogs becoming bored and distressed and having to be rehomed.
No responsible rescue charity would allow you to adopt a puppy, although some of the European rescue dog charities apparently do, which is crazy. Breeders are also often less scrupulous. It's a red flag if they know the ages of your kids but will sell to you/allow you to adopt anyway. Any decent charity or breeder knows that sending a puppy to a home with young children is a huge gamble and it often ends badly.
If you must get a dog while they are this young, get a calmer, adult dog who can live with children. Avoid working breeds such as collies and collie mixes, as they are hard work and need a lot of exercise and stimulation, they are not good family pets.