If it was a responsible bona fide rescue centre doing a rehoming, they would be extremely wary around the existing elderly dog and the child and would insist on meet-ups beforehand.
The fact that the XLB has been owned by feckless idiots beforehand does not augur well for it's behaviour.
The fact it's looking for a new home shows it wasn't cared for,
Probably massively inbred which compounds aggression and other issues.
Any 'Rescue' dog of any type needs time - often in the beginning they are 'Shut down'...but they are watching and finding their place in the household.
Soon they can begin to 'Flex' as they who is weak, or old, or young- I'd not want any dog with fighting genes hardwired into it around children, pet dogs or cats.
As they grow older, they often get more aggressive.
These kneejerk 'adoptions' are so often not thought out properly, so the dog gets re-homed again {Illegally} or else ends up getting shot by police or euthanised when it escapes from it's owner and goes and maul some innocent child or pet.
Lots of the muzzles one sees are just a joke- a loose single strap around the muzzle that wouldn't stop a mauling.