difficult sentence

[mella]

盤をはさんで二人はもうぶつかり合っていろんですよ
Those two are going to fight, on the squeezing sides.

[AJBryant]

It sounds like they're playing go or chess or something.

"They're already clashing on either side of the [chess/go/shogi/whatever] board."

More colloquially, I'd imagine, is "They've already started the match."

[NocturnalOcean]

盤 = Shogi board
はさんで te-form of 挟む which means to hold something in between something.
so 盤を挟む means to sit on each side of the board/have a board between them

In the following sentence, you marked a bit wrong.
the U, is supposed to be with もう =already
ぶつかり合う = clash together

So it's just like AJBryant said.