From my limited experience, boys are hideous at 10 or 11. One of ours turned from cheeky cheerful loving boy to a creature that communicated in grunts, lied through his teeth, deliberately wound up his sisters to the point of tears or fists then denied all knowledge EXCEPT when DP was around then he was a little angel, which of course meant that DP didn't see the behaviour or wrote it off as "boys being boys" whilst coming down like a ton of bricks on the others for doing the same thing. Drove me insane and it took a while for him to see the effect it was having on his son, and on the rest of the family.
For you, of course DP's son doesn't want to share his Dad with you because that means he isn't the center of attention and has to behave. He's not stupid, he knows he's got his Dad wrapped round his little finger, and that's not healthy.
I'd have a quiet, non confrontational word with your DP about the need for you both to be on the same page with regard to discipline, and that any discipline handed out had to be fair to everyone, and applied to everyone equally. Point out to him that if he allows his son to get away with things that he punishes others for it sets a dangerous precedent. In a very short space of time his son will be doing exactly what he likes and your DP will be wringing his hands wondering what went wrong and why his darling boy has turned into a selfish manipulative young man who doesn't give a toss about anyone but himself. Also, ask him how he'd feel if the boot was on the other foot, and is he aware that preferential treatment will mean that any respect your children have for him will disappear AND you will resent it on their behalf which will totally undermine your relationship.
How he responds to your conversation will tell you what you need to do next. If he's open to listening and changing how he deals with his son, your relationship has a future. If he won't, then as much as I hate to say it, it's not likely to last the distance.
Good luck.