The second MMR dose didn't even exist in the original programme. The MMR was designed to be a one off vaccine that offered high protection.
Then it was discovered that some people didn't produce antibodies after MMR vaccination. The figure given is around 90 to 95%, although despite having looked, I can't find impartial documentation which backs this figure up.
So the second dose of MMR was introduced in order to catch all those who didn't take the first time. Seems like a pretty gung ho approach to me, unnecessarily vaccinating so many children with a live triple vaccine but hey, nobody ever said that the DoH is mean when it comes to spending on vaccines that may not be required.
So, one can test for immunity to see if the child concerned has reasonable antibody levels or not. If yes there is NO NEED to have the second dose as it is only provided with the intention to catch those who didn't convert with the first dose. The first dose is not rendered useless if the second is not given.
If child tests negative then a real decision needs to be made IMO. Perhaps the child is a non taker (person who doesn't convert no matter how many vaccines they are given) in which case it is pointless to jab the child again. Perhaps the child had been immune but is no longer (this to me would mean that the vaccine is not very good and there is little point in having it again).
Perhaps the child will develop antibodies after the second shot despite not having done so after the first one but there is no way of knowing for sure.
Then there is the option of going for well spaced out singles with ONLY the vaccines which could benefit the child (so not rubella for a boy and none of the others for anything your child tests positive for).
That's how I see it anyway, although personally I wouldn't vaccinate any member of my family with the triple vaccine no matter what the results of antibody testing.