Help! Male dog won't stop peeing in the house because of new male kitten.

Sorry for the long post, but I can't find tips pertaining to this particular situation ANYWHERE and we really want to address this issue now!

My boyfriend and I have two dogs that he has raised since they were puppies. There is one male, Jaks (5 yr) and one female, Eva (6 yr). Two days ago we got a male, 9 week old kitten named Binx.

Preface: Jaks, our male dog, is fully potty trained and rarely ever goes pee in the house. The only time he has done it consistently was when my boyfirend lived with a roommate who had a male dog. Jaks is definitely a beta male, so we think that he used to pee out of anxiety/territorial/wanting attention when the other male dog was around. We didn't even think this would be an issue with a cat! So heres what's been going on:

When we first introduced them, we put Binx into the bedroom and put Jaks and Eva in the living room. We gave Jaks and Eva bones to distract them and put up a baby gate in-between the two rooms. Jaks was the first one to notice Binx, he came over to the gate and sniffed, and Binx tried to climb the gate, so I picked him up and they sniffed each other. Binx was raised in a house with two dogs so he was really relaxed. We brought Binx into the living room and put him on the couch and Jaks sniffed away and they were fine with each other. Jaks obviously kept following him around to sniff him but it was all very amicable.

That night, I was playing with Binx and Jaks and Eva were on the bed, Jaks jumped off the bed and started peeing. I assumed its marking his territory so I shooed him outside and cleaned it up. Then in the morning, Binx kept trying to go up to Jaks bowl while he was eating and Jaks growled him away. I let him do this because I think they need to establish their stance between each other. They were fine all day yesterday, until last night.

I had 2 friends over and we were sitting on the couch. Binx was on the couch and my friend was playing with him while I was on the other side of the room. Jaks started peeing again next to the couch so I shooed him outside, cleaned it up, and then scolded him.

Not even an hour later, Binx went up to Jaks food bowl and I would pick him up and move him into the bedroom in front of his food bowl, this went on about 2 or 3 times. The 4th time he did it, Jaks started peeing again. I shooed Jaks outside and cleaned it up and then sprayed Binx with water when he tried to go near the bowl.

I talked to the vet today and they suggested lifting up the dog bowl whenever he is finished eating so Binx can't rub his smell on something that is clearly Jaks territory.
Has anyone had this issue before? I know it's only been 2 days but because Jaks has done this before with another male dog we don't want it to become more of a habit. Is there a way to positively reinforce that peeing in the house is not ok? We are trying to give him extra attention to ensure to him that he isn't less loved because of this new animal. Yelling at him and making him go into a separate corner when he pees doesn't seem to work. We don't want to put him in a crate because my boyfriend crate trained the dogs in a way where the crate is their safe place, not a place of punishment, so we don't want to change that. The kitten hasn't peed anywhere since yesterday. He does have trouble using the litter box but I think that is more out of still being young and needing training rather than territorial.

His territory has been invaded and he is confirming his space.

Close eye needed to catch the leg-lifting at the first sign and taking him out to the garden/yard.

I doubt very much that it is a need to go, rather a reassurance that his space is still his own

Stand with your dogs while they eat and make sure that the kitten can't interrupt their eating. Put bowls away as soon as they have finished

Hopefully, as they all settle down, things will improve.