I think you'd be throwing the baby out with the bath water to end an otherwise good marriage over this.
I feel for the kids - they are being expected to slot into their parents' lives, with little thought from either mum or dad as to what's best for them or what they might actually like.
As hard as it is for you (and I have genuine sympathy - it's terrible to feel uncomfortable in your own home) imaging how it feels to be 13, effectively a guest in your dad's house, to feel like it isn't your home and then have to go 'home' to mum's house where there's another (not chosen by him) step parent.
Im not excusing the rudeness, but I think this needs professional intervention - some kind of therapy for this kid, so he has someone to express his feelings to.
In the meantime, dad needs to spend a lot of time doing things just one to one and you need to continue being kind and polite and try not to take it so personally because I really don't think this is about him hating you as a person. I'd want my dh to make sure everything is okay with the step dad - if DS has only become withdrawn since mum remarried, I'd want to know the step dad isn't an abusive arse and no one has picked up on it to protect DS.
Re the daughter, her dad needs to book her some proper riding lessons and if this is a genuine hobby, look into getting her a horse of her own or one she can ride regularly. I know it's expensive but if you and Dh can afford a horse each then there's clearly money and so something has to be done to make her feel part of this hobby and not a bystander. She is also fitting around the lives you and Dh have built and she needs to feel like it's her life too and that she doesn't just exist on the edges.
Dont know what the relationship with mum is like but Dh needs to be talking to her and they ideally need to be working as a team to fix whatever is going wrong for their children.