Large national rescues won't rehome with young children. They're too afraid of adverse publicity if something were to happen.
Google smaller rescues near and far. They are usually more flexible, often have all/most of their dogs in foster, so can be assessed in family situations. They may have a slightly different selection of dogs. Think about a slightly older dog (above 3), puppies are far too much work! Join any FB groups the rescues have, much more up to date than websites.
Look at:
Black Retriever X rescue
Hope Rescue
Four Paws Rescue
Balkan Underdogs
Help Pozega Dogs
Heathlands Animal Sanctuary
Holbrook Animal Rescue
EGLR
Silver Fox Dog Rescue
All have FB groups. Expect to be proactive and keep in contact with rescues. They simply don't have the time/manpower to keep on top of every message/email/phone call so it helps if you can be proactive without being a PITA!
Think about days out, holidays, after school clubs, weekends away - dogs do restrict your ability to do certain things as they can't be left for too long. Are you happy with this? Friends/family who could help or would you need to pay each time for a walker? Insurance, food, vaccinations and boosters, it all adds up monthly.