I think you're getting a hard time on here OP but it does sound as if you didn't do your homework and had no idea what you were taking on with JRT.
They are terriers so they are going to be hyper and pretty stubborn. She needs to be properly trained and the whole family needs to be consistent with her training.
As pps have said at 7 your DS is old enough to understand that he must not wind the puppy up and make her hyper. He might not intentionally hurt her but at 4 months she's still very small and if they're running around and a bit out of control he could accidentally tread on her, which would be awful for everyone.
Have you got him involved in her training; he can teach her to sit, stay, come and to do simple tricks. You might find he gets real pleasure out of the dog responding to him in a positive way, rather than just running around mindlessly.
Agree with pp that rehoming with you DM doesn't sound like a good idea. Seven cats and a JRT sounds like a disaster waiting to happen.
To give up on her so soon, and it is very soon, which is the reason you're getting the harsh responses on here, is a bit odd tbh. Did you do no homework before getting so you understood what you were taking on? Puppies can be hard work, and terrier puppies are probably the hardest.
You need to put in the work if you want to have a well balanced adult dog, otherwise, yes rehome her, preferably back to the breeder while she still young enough to find someone who understands what giving a puppy a forever home means.