Sh** happens, it ain't your sh** in this case so ride it out. It's comes with the territory.Then you tried, mistake. If PU wants your advice, give it to him but let him sort it out.

I did - he made final determination after we talked - still they wanted me to change things because they were both pi$$ed at him.

The only thing that *might* be different in the OP is to have the umpires decide what to do, and then get both coaches together and explain it to them at the same time. Maybe include the "yes, I messed up" comment from the PU, and say "there's no way to know for sure what would have happened, no one is going to be entirely happy, but we're going to put this runner here, that runer there."

not a nother thread but...

Say PU calls a strike. Can Home Coach appeal that? If not, and PU says there is an out how can we change that? I do believe you have to stand by your partner as a team out there. However, I would say that we have three outs and the play is over. I realize HTBT but you could argue the catcher heard it and let up on his throw that got a way. That could be the reason that the ball was overthrown.

Sounds reasonable, getting it right often requires eating large helpings of crow and taking the heat for stepping up to your ethical responsibility.

Much like taking a clearly minority opinion on a forum regarding ethical behavior of umpires - but that's just me. Taking the heat for the greater good. ;)