I want to get a dog but I have to work, how does everyone on broadway market do it ?

Owen has a nemesis, and his name is Barry*. Little welsh terrier dude, they used to play quite nicely but at some point in Owen's nascent adolescence (maybe at 9 months old) Barry absolutely flipped and now Owen cannot be allowed to go un-aggressed. He will run the entire length of the park if he happens to catch sight of Owen whilst off-lead, growling his little head off. Normally his owners will clock us first and put him on lead, at which point he'll run to the extent of his lead's length and growl and bark. It's generally mildly entertaining when Barry's on lead, but if he manages to find us when off-lead it's pretty grim. Owen is naturally submissive so goes down and the little cunt gets all up into him/over him with horrible growls and barks. At this point I grab his collar and basically drag him off, looking at his owner's with mild exasperation. When this happens, The bloke owner is very apologetic and that's all fine, I don't need apologies, dog are dogs etc, but a bit more urgency would be nice. It happened this morning with the lady owner and she just ambled across. When I offered her the still-growling and trying to attack Barry, she just said 'I really think we should just let them sort it out between themselves'. I very nearly lost my shit, but the presence of some other owners I like made me keep control. That is a totally dick-ish thing to say, right? He's a puppy. He has never shown any aggression to anyone or anything. When other dogs aggress him, we usually get at least 24 hours of stress at home, panting, obsessive licking and often barking overnight. The last thing I want to do is let him get stressed/scared to the point of agressing back at Barry. Nor do I want to let Barry's aggression go unchecked, I've seen the damage Welshies can do when they get stuck in (our trainer has a massive scar on his chest from his little cunt). And lastly, Owen's a big idiot. I have done everything possible to keep him from any aggressive behaviour - you just can't have a big dog with those sort of behaviours. TBH if Owen acted like Bary was he'd be muzzled and on-lead at all times. I totally get that this must be really annoying/upsetting for Barry's owners too, and she'd love it if they just 'sorted it out themselves', but it's massively unreasonable to expect me/Owen to accept that. I know also that there are other scenarios when that is best (yappy puppy being 'put in their place' but a dependable older dog or - something I have encouraged - annoyingly sniffy adolescent being told off by a reliable older dog) but this doesn't feel equivalent to me. Maybe I'm being unreasonable?

• - no names have been changed. Barry is a cunt and will never read this.