For travel hockey, you'll have two linesmen and either one or two referees. In situations like you described the linesmen go in as a team, but the refs stay back and use a riot pad to write down numbers and infractions.
For two official games or men's leagues games, I've been guilty of going in to try to break things up myself in the past and understand the instinct, but I think it's better to just stand back, use a loud whistle and your voice to try to get them to separate and write down numbers and infractions (much like a ref would in a hockey game with a full officiating team). If someone is down on the ice just getting destroyed, then you go in with your partner, but if it's all wrestling or even fights, the better option is to just record the infractions, let them tire themselves out and only go in if someone is at a real disadvantage.
When summer/fall hockey briefly returned in my area last year, rules were written that stated referees would not physically engage with any players due to COVID and would use their voice and electronic whistle and record the penalties. In men's league, this is probably how it should be all the time in most situations. In leagues where you have refs and linesmen, sure the linesmen can go break things up (even then you want to wait until they've tired themselves out a bit unless someone is at a severe disadvantage).
Calling penalties early can be helpful, but sometimes things will get heated anyway. In hindsight, calling the hook early may have been better. Even if you called it late, you might get some whining over a late or soft call, but at the end of the day it's only a 2 minute minor and may have sent the message that you're seeing and calling infractions.