This is an abusive and controlling relationship that you are in, as well as subjecting your children to it.
"...think older kids/early teens clashing with alternative father figure- recipe for disaster but I naively thought it could work. I have learned my lesson..."
Does n't look like it. It isn't working if you kids need to make themselves scarce in their own home when he is around. So for 5 nights last week your DC were walking on eggshells and hiding in their bedrooms.
"kids tolerate him"
Thats not good enough for your kids. They are v young and have already been subjected to a family break-up, endured a "clashing father figure - recipe for disaster", endured another relationship breakdown where their mother was cheated on and left with money issues - then THEY are punished by this evil person who steals their pet and refuses to give it back despite police involvement. Beyond cruel.
"He's still refusing to acknowledge my point and still if the opinion that because it was a Saturday, I should somehow have put him at the top of my tree. I feel like he's really out of order for stropping about this - but every time I try to get him to see my point of view he shuts it down by telling me he doesn't want to get into an argument."
Controlling, uncooperative, sulking, stone walling, abusive behaviour.
"There were some things that he did which have given the kids reason to give him a wide berth and although I still love him and I'm willing to give him another chance, I'm aware I don't have the right to expect the kids to do the same."
Plenty reasons here for anyone to give him a wide berth - not just your kids. No you dont have the right to expect the kids to give him a 2nd chance - but you are imposing this on them by having him in your home and demanding your time away from them.
"And they are respectful. They aren't rude, They just don't want to hang out with him!"
Shame OH doesnt have the same qualities that you expect from your DC. By his actions and your submission you are teaching your children to tolerate and accommodate bad behaviour in their own home.
"First my eldest son has the biggest problem with him. He's polite and will be respectful but because of dog issue, he'd prefer not to spend the evening with him, and would just go to his room if OH was here." Poor kid spent the last 5 out of 7 nights banished to his room.
"they are respectful and know that wilfully being rude is not acceptable." They must be confused because this behaviour (and much worse) is acceptable to you from OH.
"They found it all very upsetting." Did you find it upsetting yourself or to watch their distress? If so why have you erased that hurt? What has he done to make it up to you kids? Does he still see that he was right to kidnap their pet?
"There was money and another person involved." "I'm trying very hard to move on from these issues" - Looks like you are trying very hard to absorb them - moving on would be getting rid of this nasty individual.
"but I'm trying to focus on the current problem"
This is where you are going wrong. Look at the whole story, put it together, what do you see? What does he have to do worse than being a routinely bad adult in your DCs lives (clashing), having an affair, causing money problems, pulling the dog stealing stunt and causing immense distress and trauma to your kids, arguing, sulking etc when you want to spend time with one of them for the first time in OVER A WEEK when he has been with you all of this time?
Do know how much lower you can go here? Do you have any red lines?
"I've spoken to the DC and made it clear to them that he will not be moving back in because it wouldn't be appropriate or fair for anyone" - but he is there already.
"as long as he doesn't pull the same shit."- but he is and he will and he continues to do so.