dog related..help?

hi everyone

so its a bit of a long post but im really at a loss.. i currently have a 12 week old dog she is quiet but poops and pees all over the house.. we can take her outside for an hour she does nothing bring her in the house and she will do her buisness.. i also have a 2 yr old he is constantly yelling for the dog to get off him she jumps at him nips his hands really whatever she can get her face near.. today he was sitting minding his buisness and she decided to growl and try to bite his face( she missed as we got her just after we heard her growling) well that was enough for me i put her in her bed and thats where i intended to keep her. my son then decided 10-20mins later he wanted to snuggle with her so he let her out and they were fine the he started to walk away and she started nipping at him again ive tried everything i can think of to get her to stop all these things but nothing seems to be working. we had a dog previous to this one and we got rid of him for pretty close to the same reasons he was just a bit worse since he was the main one for a long time before we had our son so now im stuck because it took my son a while to get over the male dog we got rid of the first day he threw his whole dinner to the floor and refused to eat because buddy wouldnt come try some. i know this dog probably needs a new home but what do i do about the heart ache my son will have i feel horrible he loves dogs but this little 12 week old it a handful any suggestions if you made it this far would be great! how do i get her to stop do i just re home her.. she is a tiny dog it is the puppy of the male dog we had previously.. she is a pug/maltese terrior/jack russell/ westie if that helps ... i know in my heart better safe then sorry and she needs a home but my poor little man is going to be crushed.. 😭

EDIT

TO clarify.. i came in search of advice on how to help to train the dog forbthe washroom behaviours as stated we take her aout and can be out for hours she does nothing come in and she goes.. we have tried treats when she goes outside which was like twice.. and as a ftm with a dog it is concerning with the biting.. again was looking for advice to stop the biting.. iforgot the the women of these groups are pperfect no flaws or concerns just judgement to others. yes if biting continues i would need to rehome as my sons safety is my main concern unlike some people my child comes first was simply looking for advice sure wont do that again.