I know what you meant about control, and I've been known to get a bee in my bonnet about "controlling" parents in the past. It was clear that you don't expect her to be a little obedient robot, don't worry.
I agree that missing a bath is a strange and counterproductive threat/sanction.
I think you need to have a serious talk with him. I think it can be good when parents have different approaches. DH and I certainly do. I found it difficult at first, because I was brought up by a single parent, so it was outside my range of experience. And when I spent time with my dad, although he was different to mum, my stepmum and he were very similar in their attitude and approach so I sort of learned that as the norm, if that makes sense. Whereas PIL are still together, and had very different parenting styles. DH explained to me that this is very helpful for a child because they can see different approaches in practice. It does, however, depend on three solid things to be in place. 1, that you always back up anything the other has said if they come and ask you, 2, that you don't undermine each other in front of the children and 3, that you agree on the ultimate boundaries/rules of what is OK and what isn't OK in the house, you're singing from the same hymn sheet, as it were, even if you're the soprano and he's the tenor. You complement each other. If and when you do have issues about how the other is handling something then you talk when you're alone, never in front of them.
So talk. You need to agree broadly on what kind of behaviour is OK and what isn't and where the boundaries lie. They can vary a little bit - DH is more tolerant of noise whereas I am more tolerant of mess. When a boundary is approached or crossed, it needs dealing with. Ignoring is not dealing with something - it's neutral. It's fine to use ignoring as a discipline strategy as long as it's coupled with something, like high praise for doing the right thing, a lot of micromanaging and signposting, other encouragement to do the desired behaviour etc. But ignoring everything or ignoring plus punishment/threats is not an effective strategy, it's just doing nothing.
If you're going to do sanctions you need to agree what the sanctions will be. If they are vague then put some things off limits - for example some people say that the bedtime story is off limits for a sanction. Others might say that a reward the child has earned for being good can't be removed as a sanction. Things which affect others, e.g. cancelling a playdate, might also be off limits. And of course a lot of people decide that physical punishment is off limits.
The Team Daddy thing (and bad cop) have to stop. Anything like that is undermining you, and yes you are totally right - he is doing it because he is picking sides, perhaps scared of losing that relationship with them. Unfortunately, he's throwing you under the bus to do so. Every time he puts himself on a "team" with the children against "bad cop", he's painting you as somebody bad or scary, which is just totally selfish as well as being unhelpful. It's great that he wants to have a good relationship with them - he does not have to do that at the expense of your relationship with them. In fact to do so is so grossly unfair. He really has to get over the fear that if he disciplines them, they will stop liking him, doesn't he? Do you think he might read some parenting books (123 magic is pretty good for this "They won't stop loving you" pep talk, and is a nice easy system to learn because it's step by step) at all? Or How To Talk, Playful Parenting, if he wants something more positive. Ultimately there should be no sides. Your whole family is a team but you and he are the leaders or the coaches.
I think you need to get him to try some structured discipline tactics including giving some consequences, get him to try them out over a weekend and then witness how the DC don't stop loving him or wanting to play with him, and are just the same afterwards. Perhaps even better, because they know where the lines are more.