OK, so why was it not possible for you to just say "no, I don't want to do Christmas lunch at yours, we'll just do our own thing but if you were hosting Christmas eve we'll come."? Because by telling her it was too much work (and getting your mum to join in would probably feel like 'ganging up on her') you were being bossy.
You didnt tell her you didn't want to do Christmas dinner at hers, you told her she was wouldn't be able to do it for everyone. You essentially told her not that you were declining your invitation, but you were withdrawing her invitation to everyone else on her behalf.
It doesn't sound like she's thrown a tantrum, she's just not contacted you, and as you were the rude one, the onus should be on you to contact her first to say sorry.
You didn't want to see her Christmas day, what you wanted her to do was host a big party on Christmas eve, sounds like she's decided not to do that either. You can't make her host the events you want the way you want her to, only accept or decline the invites you are given, and issue invitations of your own.
Anything else is bossy, rude and controlling. It might just be you two are a little more alike than you want to admit? 
Call her and say sorry, that you didn't mean to piss all over her parade and realise it was rude to tell her she couldnt host Christmas day. You didn't mean to suggest she wasn't capable or shouldn't host the day any way she wants. Can you ask her if she'd like to come to yours over Christmas? Make it clear you are asking her first - not that you are taking over Christmas eve or hosting a 'rival event' that family have to pick between.
Next year remember, the answers to an invitiation to spend Christmas day/eve/boxing day etc with someone are "that would be lovely, what would you like me to do/bring?" or "Sorry, no, we have other plans already/we want to just be the 4 of us, but thank you for the invitation, hope you have a fabulous time!"