Rehoming puppy…I don’t know what to do.

I have a 4 month old puppy that we rescued 24 days ago. I have a 3 and a half year old son. The puppy is constantly nipping and grabbing at his arms, legs, butt. My son could just be sitting watching tv and the puppy will just go up to him and start grabbing. My son will say ouch and yell to me to help him and pick him up so he can get away from the puppy. I can be holding my son and the puppy jumps up to grab my sons feet. I had a trainer come and she gave me suggestions, I’ve watched videos on ways to help. So far nothing is working. I feel like I’m constsntly intervening, redirecting and then having to separate the dog. I’m exhausted with it all and hate that I’m feeling this dog shouldn’t be here. When he’s not nipping my son loves him but the nipping becomes very overwhelming. I never thought that I would be considering rehoming or giving the dog back to the rescue. I don’t know what to do

Please remind me of the benefits of having a dog.