Christmas Cards Dilemma

You could just use first names. Bob & Sherry & Cloe

I'm on board with everyone else... why the formality?
Keep it simple,. Bob, Jane and Nancy...

Do you send Christmas cards to people who don't actually know who you are? I would assume not - in which case there is no need to include last names at all because they know who you are. In my house, we have different last names simply because I chose not to change mine. Our Christmas cards are signed like this:
Happy Holidays!
Jim, Jane, Joey, and Jason

I wouldn't do last names on the inside of the card. You're making more out of this than needs to be.

You're sending out cards to family and friends - people who KNOW the situation, right? Not strangers? I would say

Merry Christmas from C., John and Sally.

Done. no one's feelings are hurt. No stress.

I don't see why the last names need to be on the card anyway - you're only sending them to people you know well and who know whose daughter she is, right? So just put "C., John and Melissa", or put your husband's name first so that yours is next to hers ("John, C. and Melissa"). If you insist on last names, it's okay to write "C. & John Smith and Melissa" but I think it's a little more cumbersome. You can put your last name on the return address label on the envelope and leave it off the card entirely.

I've seen "From our family to yours" or that kind of thing. Or even just your names (like first names).

You can just sign it, Bob, Mary & Sally, no need for last names.

Use the KISS method: Keep It Simple Silly.

Merry Christmas from Steve, C. and Mary.

We have two last names in my family as well. My oldest son has my unmarried name (let's call it "Smith") and my now-ex, the kids we have together, and I are "Jones." I use the "Smith-Jones family" on our holiday cards, or just list our first names. I wouldn't be concerned that using just your new name is disrespectful to her dad, but I would be concerned that it's disrespectful to your daughter. Her name is her name, and it should be reflected in how you refer to your family. I actually use Smith-Jones on anything that reflects our family...answering machine messages, wall hangings, etc. because my son is just as important a part of the family as those of use who share a last name.

I agree with Jennifer.