Hi I'm new to all this and don't know where to turn stumbled across this page on google and thought I would give it a go. I've been with my boyfriend a year and a half and lived with him for about a year (yes we moved quickly) I'm 33 years old no children of my own, he is 38 and has a 13 yr old son and 9 year old daughter. He has them every other week night and every other weekend, so 50% off the time. The daughter is lovely, a bit over bearing but a really nice girl, the son however I cannot stand! At first he was fine seemed a nice kid, but now he causes nothing but issues for me, he makes little digs and comments about me or to me and I know they seem ridiculous but it really irritates me, comments like "what is that you're wearing" or " Dad is over us not living here all the time I mean not over Mum but us" or "the thing is he won't even use that" regarding presents I have bought his Dad, I know they may seem silly but it's happened quite a bit and I keep getting told I'm being too sensitive or I'm taking him wrong or he doesn't mean it like that his only 13 he don't realise what he is saying, the thing is one of the times he then lied about me and tried to say that I had said something bad about his Mum to his sister which I would never do and my boyfriend knows this but did nothing about it and still says to this day that he knows I would not lie but he doesn't believe his son knew he was lying and that he generally believes I had said something about his Mum, which to me is ridiculous and caused me to leave and stay with my parents for a few weeks to get some space, during this time I missed my boyfriend terribly as I do love him dearly and I went back. It's been 3 months know and there has been a few more comments with no consequences or responsibility given to what he has said. Now though he has started bullying my nephew (5 years younger them him) I am extremely close with my nephew and class him as the closest thing I have to a child, my nephew plays with him online with a few other kids too, at the weekend he segregates my nephew from all his online friends, tells him he is going to do this and threatens my nephew that he will tell me my nephew has done stuff to try and keep him quiet, my nephew is heartbroken and has lost all his friends to play with online whilst we are in the middle of a lockdown and is now lonely, my nephew lets me know this has been happening for weeks but it hasn't wanted to say anything and lose his friends and that he has been using me for weeks to threaten him, I am livid with this and quite frankly completely hate this child now, I air my issues to my boyfriend who tells me to pack my bags and leave, he is not seeing that his son is a bully and what he has done to a child younger then him and me providing proof of him trying to turn his friends against him and get them away from him, I understand he cannot solely believe my nephew and not his son but when I have given proof and given there is such an age gap am I wrong for thinking something should be done about this? 
I love my boyfriend and it completely breaks my heart to be away from him, he is telling me he loves me and asking me to come back, but can I really continue to live somewhere where nothing is done about this child and with how much I hate him now? Anyone had anything similar and have any suggestions?

apologies for the long past or if anything is phrased wrong first time here and first time being in a relationship with children and I'm completely lost