Some of what you are asking depends on the rescue's policies.

Some will accept the dog back, label her / him for a "no children" household, and attempt to place her again.

Some will remove the dog from their program and find a rescue which does cope with dogs which can't be around children. The dog will be placed in a boarding facility / kennel until such a rescue can be located; but this usually has a time limit as they can't afford the fees for long.

Have you seen ANY problems with the dog around adults? This will be important when you contact the rescue.

What age are the children the dog has problems with: under age 6, under age 10, this is often the case with rescue dogs, they can't cope with the sudden movements of small ones.

Some rescues do just have the dog PTS.

Policies, their current funing levels, their rate of dogs coming into their program, openings in their foster homes, the specific background of the dog, the dog's age, all these will factor in to the decision.