THUM,
I really think you need to listen to your DHs side fo the story. From what you have posted, you and he haven't really talked about what has happened this evening. I am thinking that if your cousin gave your MIL the invitation and she told them that you couldn't go, could she also have told your DH that you weren't invited for some baffling reason and tried to manipulate the situation/your DH from both angles?
Of course your DH could have/should have raised the subject before but if he was trying to spare your feelings and was between a brick and a hard place then I do actually feel for him as well as you right now.
I think when you have calmed down, you need to ask your DH to explain exactly what was said and what went on, to hear him out without any interruptions or prompting so you have a very clear picture of the whole mess.
I would then suggest your DH needs to decide where his priorities lie, with his mother or with his wife and the mother of his children. If he decides you, then I would suggest your put a brave face on and go to the Christening and present a united front as your family unit (DH, you and DD) and that DH has a word with his mother that you are his priority, that he nearly lsot his wife over her scheming.
It is up to you how you play it with your DGD, but personally I could not use my own child as a pawn in family rifts as kids want to see their GPs and she is your DHs mother even if she is a bitter old witch.
Just trying to offer a balance to the string him up by his bollocks view...