Why is the Prince upset about the "ancient citizens" becoming involved in the feud?
I think the Prince is just generally angry that the Montagues and the Capulets have disturbed the peace for no good reason, and without any sort of obvious cause. It's just an ancient grudge - about what, we don't know! Here's what the Prince says:
And made Verona's ancient citizens
Cast by their grave beseeming ornaments
To wield old partisans, in hands as old,
Canker’d with peace, to part your canker'd hate.
So the old pensioners of Verona city have had to throw aside (cast by) the "ornaments" which might suit their graves, and instead pick up and wield "partisans" (a sort of bladed weapon, quite like a sword), in their old hands. Why? To part the Montagues' and Capulets' cancerous hatred.
It's understandable that the prince is annoyed that these poor old people have had to come shuffling out to call a halt to proceedings. Perhaps he himself is supposed to be old (no clues in the text). Though the key point is that there's something vaguely ridiculous about grandma and grandad coming out to split up the Veronan feud. The Godfather this ain't!
Hope it helps!