Do you have court orders governing your divorce? I know you just filed, so maybe not. Have you had your mediation yet?
If you have any sort of court orders yet, those set the legal framework with which you and your ex must both abide. Although are you U.K.? I really am not familiar with those legal issues.
If you do not, you and your stbx are in no man's land. Since you have filed for divorce, anything you do from this point forward (and past, but especially now, going forward) is subject to the court's scrutiny. If you and stbx do not agree on what's best for the children, and the court must step in and decide for you, courts generally favor maintaining the status quo of the children, and they always want to see the parents getting along and fostering a relationship between the kids and the other parent.
Naturally, when you separate into separate homes, there is a change in the status quo. But as much as is possible, while still fostering/encouraging a relationship with the other parent, courts favor keeping the kids' routines the same and their lives as stable as possible.
Unfortunately, as painful and as hard as it is for those of us who want to protect our kids, the courts generally do not care if the other parent has a BF or GF, and they generally do not weigh in on how/when/if the kids interact with the GF or BF, unless the person is maybe a hardcore drug addict or sex offender or something. Generally, courts stay out of it.
So until you get court orders, any parenting behavior you want your stbx to abide by, if he does not agree or does not want to, you are SOL.
HOWEVER, since you're both being "observed" by the court at this point, this is where you are aware of and document his behaviors that have a negative impact on the children, if not outright harm or abuse.
I will also say that my separation orders included a clause that neither NPDxh or I were allowed to have DS in the presence of a 3rd party romantic interest. That clause dropped out of our divorce agreement, and I'm not sure if it being in the separation orders was standard, or if NPDxh pushed to have it in there. But if it was the latter, it's rather ironic, considering he got a GF ASAP and promptly exposed DS to her and did the same thing --- had DS spending nights there, etc. -- when NPDxh and I are barely divorced ourselves, and with all the upheaval and instability that that brought to DS. I asked NPDxh not to, he basically told me to go screw, and 3 months later GF and he were broken up, and DS wonders where she went.
So I was unsuccessful at getting NPDxh to modify his behavior for DS. It sounds like from what you described, your stbx would be pretty resistant too. But if you know of some way to get him to, I would try that, since I think it's unlikely that the court is going to.
If your 3yo is having anxiety issues because of her father yanking her around like that, I would certainly document that with a health professional, and that could be helpful to you.
As for the behavior concerning the table ---- we all have different approaches to how much, and when, we tell our kids. I will say that if you choose to decide to talk about the behavior, it's best to focus on the behavior, and not the person.
It sounds like with the table incident, that's more of a situation that disturbs you (and understandably so), but not your son as much, so I would let it go. He might not have put too much thought into it, and if he has, for all he knows, you and his dad came to some kind of agreement or something. Even if he picked up on the sarcastic comment (he most likely did; my 4yo can pick up on it), again, it's not something he probably spent a lot of thought on. Just boring grownup stuff.
I think DS is being groomed to idolize his NPDxh dad too. DS can love him and think he's great all he wants. But I will absolutely have no problem, if it comes to it, of pointing out bad behavior, having DS recognize it and being able to deal with it, just as I will in regard to all of the people in his life. I do not want DS to have the same twisted sensibilities and distortions that NPDxh does.