And definitely want to keep his mum out of it. Tends to wind me up as I feel my parenting and my kids are being criticized. She suggested that my kids might be trying to get him into trouble which isn't the case.
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)
I get this with my DSD7 too. She can be very mean to my DS5. She's OK with DD2 but openly writes in her school news book that she doesn't like her half-brother and she does lots of nasty things to deliberately upset him. He's her main rival when she's at ours atm, I'm expecting the behaviour to extend to DD2 in the none too distant future though..
Until a couple of months ago my DSD was an only child at her Mum's house and I think having to adjust to not being the only child when she's with us is a big part of the problem - she doesn't like it.
Fortunately for us, I've been around ever since she can remember and she doesn't seem to begrudge her Dad spending time with the other kids.
I don't have any magic answers; the jealousy is probably always going to be there to some extent. What we do is be consistent and fair wherever we can. There isn't an excuse for being unkind to other children as far as we're concerned and she gets punished every time just as we would punish DS if he was nasty to her.
I wouldn't make too many allowances if I were you; it's not fair on the other kids in your home. Perhaps a chat from Dad explaining that he's not going to be the centre of attention all the time and that nastiness is not acceptable. Some regular time on his own with Dad (weekend hobby or something of that ilk more suited to a 7 year old than a 4 year old?) may also help soften the blow. Martial arts maybe?? Football? I'm not that up on 7 year old boys but I'm sure there's something. My DH takes my DSD to a performing arts school each weekend while I do something different with the younger kids.
My dp is moving in with me and my dd7 and ds4 next month and his ds7 will be living with us half the time. He is lovely but he as an only child he is struggling with sharing the attention.
We've just been on holiday as a family of 5 and on the whole the kids got on great but there is some clear rivalry between two boys. My dd and dss get on really well and sometimes my ds gets a bit left out. My dss finds it hard that to accept that my ds as a younger child needs some concessions e.g. if we give him a chance in a game dss doesn't like it etc. He also doesn't like it when my children have cuddles or play fight with his dad. There were a couple of times I had to ask dp to have a word with him over things he had done to my ds e.g. messing up his sandcastles
Also dss has told his mum that he gets told off unfairly over my ds. This came after he was saying he hates my ds and me and dp told him that was a hurtful thing to say.
Just want to get the balance right. We can't let him get away with being unkind to my ds but equally we want to be understanding about his feeling as he gets used to being a stepbrother and not the center of attention.