Dalton is there to make sure nobody makes the same fuck-up as in the last Grail War. The crest is a bonus.
Rayneth is there...well, frankly, because she's a foolish child who is literally joining a war because she wants to see what it's like.
Rei's there because his family wants to be all tough and win the war. 

Frankly, that's not TOO unlike what the Fourth Grail War was.