We've had a bit of trouble with jealousy between our two youngest - my DD and DSS. They were 7 when they met, and are now 10. Neither were only children, but both were used to being the youngest in the family and found it hard to know how to a sibling-type person who wasn't older than them.
My DD was really jealous of me doing anything at all mumsy with DSS and would say "you're MY mum, not his". Sounds like your DSS may be feeling a bit similar that he doesn't like sharing his dad.
And DSS was quite territorial, and when we spent time round DP's house (before moving in) and my DCs didn't have anywhere to go to, so DD would bother DSS and wind him up, then he would prod/poke/hit her and she would come crying to me. They also declared that they were "mortal enemies" to all who would listen (school friends, etc).
It's actually loads better now, and DD and DSS play a lot together, so we must have got something right :)
At first I tried to avoid doing too much mum-like things with DSS when DD was about. But I also tackled the issue head on asking if she was jealous of me being like a mum to him - she seemed so relieved that I'd asked and helped her articulate what was wrong, and after lots of reassurance about how special she was to me, seemed better after that. DSS just got better naturally after we moved in as DD had her own room, and he was sharing with my DS (who he gets on fine with).
When we moved in we set out a list of "house rules" and it's still pinned on the fridge. The kids also devised their own "bedroom rules" enthusiastically which, most importantly to them, allow them to ask anyone they want to leave their room. The house rules also covered fighting, damaging possessions, "borrowing" without asking, etc.
We just ignored the statements about being mortal enemies, and they seemed to forget about it after a few months. I think it's best not to get too upset by big statements about hating each other, hating you, etc - they're only young children and they're just articulating how they are feeling right now. Best to accept that that's how the feel but not to be hurt by it and remember that they won't be feeling the same in a few days time (or even a few minutes time).
They still fight sometimes. DP and I each try to discipline our own DCs as much as possible, though it is hard sometimes if you feel your DC has been treated badly.
I would try and encourage your DSS's mum to stay out of things - encourage DSS to talk to his dad (or you) if he feels he's being hard done by at your house as it's unlikely to help for her to get involved (except maybe to help her DS to tell his dad how he feels)