Can you explain how does it work?

This is from the extended FAQ-excel sheet, make by Umbrates, which answers a lot of minor rule-related problems.

"During a battle, House Cards are revealed simultaneously and any appropriate text abilities resolved. There are instances however, when the order of text resolution can be important. Here is the House Card resolution sequence for resolving all such conflicts:
1) House Cards are simultaneously revealed.
2) Any “Ignore” or “Cancel” special text abilities are first resolved in the player order of the “Fiefdoms” influence track. Once an ability that “ignores” or “cancels” takes effect, it remains in effect for the entire battle.
3) Other appropriate text abilities are then resolved in the player order of the “Fiefdoms” influence track. The special text of the first card is completely resolved and implemented before the second card.
4) After the outcome of the battle is determined, any “If you win this battle…” or “If you lose this battle…” special card abilities are resolved in the player order of the “Fiefdoms” influence track. The special text of the first card is completely resolved and implemented before the second card."

Also, the FAQ states on page 4 (under the Tyrell vs Baratheon heading) that once an ignore ability is activated is stays in effect the entire battle.

So Willias Tyrells ignore ability activates first (because it's an 'ignore' or 'Cancel' ability), nullifying Tyrion or Tywin's ability. Then it copies Tyrion's or Tywin's ability to use as you please.

Umbrates' extended FAQ can be found here at BBG. It's a bit heavy on the data, but will pretty much answer any questions you might have.