Hi OP, another one here who recommends you ask for reposting in the Doghouse.
I'm a rescue volunteer. Lots of rescues rehome dogs to childfree homes - sadly, the arrival of one, or a second child and managing the relationships is one of the most common reasons for giving up a dog, and is the reason why many rescues won't even place a dog with a family with under 5s.
There are rescues who will take your dog. There are lots of specialist terrier rescues - Google will turn up a list for you, that you will need to work through. This one is typical, and specialises in terrier breeds, and therefore really understands them. Many of them keep their dogs in foster care rather than kennels, and are careful to homecheck thoroughly before rehoming. Although it doesn't always feel like it on MN, the proportion of dog owning homes without small children (or indeed any DC) far outweighs the number of families with small DC, so finding a childfree home is not usually difficult.
A few tips for rehoming - and this is the right thing to do, given that your H is being unco-operative.
Be honest and upfront with the rescue about the incident, and your reasons for rehoming.
Do not attempt emotional blackmail (e.g. Take the dog today or it will be PTS).
Provide all the necessary up to date paperwork, including chips, vax certificates, records of training classes etc. along with his collar and lead, etc.
Most rescues are run entirely by volunteers - be patient and don't expect them to drop everything to deal solely with you. It is also very helpful if you are flexible about transporting the dog to a foster home/drop off point etc.
If the move is the real reason for rehoming, (otherwise why mention it?) then again, be honest with the rescue, if you've chosen dogfree accommodation.