How should I go about solving household dog fighting/aggression

Hello I know that it's probably best to talk to a trainer about this but I wanted to get some general knowledge and advice and possibly recommendations on where to look for more guidance.

On to the details (I am overly wordy usually so feel free to skip to TLDR): I live with my parents and they have 3 old Chihuahuas (ages estimated 12-15). We got a new dog around 3 weeks ago. Our new dog (J) is around 2 years old, neutered , mixed breed mut, and around the lower end of medium size. It's been over a decade since any of us had a new dog so we are a little overwhelmed and struggling to remember what to do.

The first two days we kept the dogs mostly separate and tried to introduce them to eachother. After those two days we let J have free roam of the house and kept a eye on interactions. J is relatively neutral towards other dogs including our own. Regarding our dogs: One (B) ignores J and J ignores her. They don't really interact at all as B is blind and ignores everyone but my stepdad. The second dog (S) is 5lb and is very twig like very small dog. He seems to tolerate J but is scared of him and cautious though its slowly getting better. J sometimes hovers to close but S has gotten used to it and mostly ignores it. While there has been no negative interactions really I am a bit concerned for reasons I'll detail later.

Our third and oldest dog (H) (also only one not neutered) is the problem. He's a asshole to everyone and is the worst behaved and even after around 9 years of living with him he still sometimes gets into a fight with S. (Neither really have many teeth anymore and don't try to seriously harm eachother, of course we still try to separate them when it happens). He has started to go deaf and blind a bit which is causing him to be somewhat better behaved but he is still a menace. He will try to lunge at J especially when H is on my stepdad's lap (and hence above J and in a 'untouchable zone') and bark at him. When on the floor H will avoid J most of the time but sometimes J likes to hover/get near him which is happening more and making things worse. I haven't kept perfect track but over the last 3 weeks H has tried to attack (and I mean on the floor trying to bite J I'm not even counting the lap lunges cuz their so common) J several times (at least 5) J sometimes reacts back but most of the time doesn't notice or ignores it. However J has instigated 3 times. The first was during the first week and when H tried to take Js brand new toy/bone (second toy we gave him, treat holder) we separated them and have been working on resource guarding with toys and bones with J (which is somewhat progressing as now J doesn't care when H steals a bone (or maybe J just doesn't notice)) The two other times were on the same day (Christmas eve) and the third time caused injuries. We didn't put up our tree or decorate until Christmas eve and probably were stressing J out. The first of that day was just H walking close to J after we kinda stressed J out by checking his nails. We should have separated them but we're to caught up in decorating. The third attack idk what caused it but J was very riled up and my stepdad had to pin him down while we got H away. H had a cut on the back of the neck and one of his legs was hurt (a leg prone to injury). My parents decided to just treat H at home as they had doggy medical supplies and the cut looked bad but wasn't bleeding really. We separated them and kept them apart the next day. My parents the day after that went on a trip and decided to take all 3 Chihuahuas with them. It's just me, my brother, and J right now. We have training classes scheduled to start for J in mid January. Their beginner classes and we are going to do them to see if they help J (he has some biting and jumping issues that are attention seeking/poor impulse control based. If the obedience classes don't help then we're gonna do more private training)

My family hasn't really talked about what to do for the dog in fighting. We have tried giving treats and getting J and H near eachother which seemed to help up until the Christmas situation. My parents aren't likely to want to pay for training for H as they kinda wrote him off as a lost cause years ago and consider him to old for any teaching to stick.

I know H is the main problem (he tried the lap lunges even the day after the attack fucking idiot) but I really only have say over J training and care. H could hurt J but it's unlikely as H is so small with few teeth. J though is three times bigger and could easily kill H. I'm concerned H is making J be more aggressive and honestly I'm really worried about the possibility of J attacking S as S would not survive any sort of attack given how small and boney he is, and I really care about S. S likes to get attention from me and the way J stares make it seem like he's jealous and I'm worried this time with just me might cause him to become possessive and aggressive when my family returns.

TLDR: I live with parents. Parents 15yr Chihuahua is a aggressive asshole who keeps attacking my dog. I'm worried this will turn my dog aggressive and lead to him hurting my parents dogs as he is much stronger and has all his teeth unlike the Chihuahuas.