If multiple players play an Order Priority Card in the same turn, the move order will be determined normally (i.e. random) between those players. The players that didn't play an Order Priority Card will also be determined normally between each other, but their first order will not go before someone who played the card.
according to this it should be A1-A2-B1-B2.
I have't tried it though, would be interesting to see in-game example