[Stumpy]

Getting the other dog fixed may help, but everything you're describing is jealously and territory things, not fighting over trim. Spend some individual time with the older dog, and if the dogs aren't hurting each other when they fight, you should just let them sort it out and be done with it. Trained fighting dogs aside, when males fight it usually is mostly posturing. Females are much more likely to kill each other.

Really when you have an older dog and bring a puppy in, there's almost always going to be some friction. The old guy isn't used to being pestered all the time, but usually they'll get used to each other and the older dog will have a second puppyhood and become more playful / happy.