THUM - WELL DONE. You did an excellent job of sticking strongly to the main points and standing your ground.
In some ways, think a good tactic would be for you, DH and DD to GO to the Christening, as a family, with your heads held high, and with DH being demonstrative that he is with HIS family - you and DD. But you will know how that would effect the event as a whole - it's obviously important that CIL has a lovely christening, but it seems unfi on her that you, her friend, should be bumped out.
MIL will not cave in easily - she will lash back, trying to get other family members on her side, and she will come u with all sorts of lies toyour DH - she will probably maintain that CIL is the ne whois lying and she didn't invite you. But that is SO unlikely that no one in thier right mind should believe it.
Keep being clear, direct and strong with your DH !
The 'toxic' book sounds good!
Good luck - you do have the strongest hand over MIL, and she must be pretty stupid realy, if she thought this wouldn't be found out! So, keep your head high and keep strong!