What would you do in this situation?

[LLPA13UmpDan]

11-12 Baseball. 2 man crew. Im BU. R1 & R2 on 2nd & 3rd, so im in C position. winning team is batting. Ground ball is hit, PU is watching third, so im making the call at first. I call "Safe, hes off the bag". I hear the defensive (losing) teams coach say "oh come on", then asks the other coach "did he call him safe?, oh no way!" He then walks out of the dugout and yells to me from beside the dugout "get help on that, blue" I'm thinking no-way. I seen what i saw, the first baseman was clearly off the bag i tell him. He then proceeds to come out of the dugout and go toward my partner. I calmly say "no coach, he's off the bag". He ignores me, and i throw him out. he then says "you have to give me a warning a first." im then like "no, there is no warnings on judgement calls" He then walks out. After the inning was over, PU tells me he saw nothing, he was doing his duties with third. After the game, league pres. tells me "the coach has the right to go to the other umpire" Im like no. What do you know about umpiring??? and that was the end of it. Do you think i was too harsh, or did i do the right thing by sticking to my call? Now ive heard of the offensive coach coming to argue that a runner was safe, but not the defensive coach to argue that the runner is out.