I have two dogs, both rescue puppies who'd been abandoned on the streets. We are not in the UK - endless stream of adorable street puppies on SM here.
It's the kids who like dogs (I'm a mad cat lady all the way.)
Dogs are now 3 & 4. Dc are 17, 16 & 14, so realistically, in 4 years' time, I will be completely responsible for 2 middle aged dogs I didn't particularly want, for several more years.
I'm quite fond of them. I will see my commitment through & look after them. They'll be responsibly & affectionately cared for, & it'll be nice for the dc to see them when they come to visit from Uni. I imagine they'll really miss the dc, though, & I'll be a poor substitute! Once they're gone, I definitely won't be getting another dog. I'm very 'meh' about dog ownership.
Would I take on a dog now, when the dc are looking ahead to independent life? Absolutely not. Tbh, with hindsight I quietly wish I'd put my foot down a bit more firmly about the two we've got - both were slightly foisted on me by friends heavily involved in local rescues, with enthusiastic cheerleading from dc.
It's a crazy time for your ds to be acquiring a dog! It would inevitably become YOUR dog.
You need to be very clear that your ex is welcome to house an entire Noah's Ark at his place, but you are very firmly not up for taking one on. No thank you, not happening.