Sorry but in your situation I don't think a dog is a good idea.
When you are considering the amount of work it takes to look after your dog - think worse case scenario then double / triple it.
So your DC likes the idea of a dog now - but I assume they are off to secondary school in September - increased homework, possibly longer travelling, extra curricular activities, different friendships - how many hours a day could you reasonably expect your DC to spend walking, grooming, training the dog?
What about in the winter when it's dark in the mornings and evenings? It's raining, snowing? Would you want your 11 year old out walking the dog when it's dark? Would you want to have to do it yourself early in the morning, alongside nagging DC to get ready for school, in the evening after a long day's work?
Then there's your partner trying to work from home - a dog may sleep for a few hours if they are tired after a walk , or bored because they are left alone- but if there's someone else in the house the dog doesn't understand that your partner is working, the dog will bark, try to attract his attention because the dog thinks s person in the house is there to play with him - or even just wanting acknowledgement - tummy rubs. Particularly if your DP isn't totally on board with the dog in the first place this won't be the ideal working environment for him. Yes, it's possible to work at home with dog there and people make it work, but that's because they really wanted a dog and are looking at how to make it work.
In a situation where it is the DC wanting the dog and one parent is ambivalent, the other adult has to accept that they are likely to be the dogs full time carer, so, at least two walks per day (one of which needs to be more than the cursory 20 mins round the block). Training is ongoing , even if you don't have a puppy there is ongoing settling in, training for a rescue dog.
Alternatively if you can afford it, doggy day care, or a dog walker would help but you would need to take this cost into consideration.