All my cards are signed from "Surly and DP", and cards to people who know DP's DCs are from "Surly, DP, DSC1 and DSC2", putting the DSCs in age order.
I have no idea how DP signs cards to his family and friends, but I suspect it's from "DP and Surly", and cards to people who know his DCs include them as well.
Mine and DP's names flow as well as they can when my name is stupid equally well whether it's my name first or his, so it's purely personal preference and ego? that means I put my name first on cards I've written.
I put my friend's or relative's name first when writing cards, and then their DH/DW, and then any DCs in descending age order. No reason really, just how I've always done it. If the card has to be posted, then it's addressed to "Mr and Mrs Surname", no initial at all. If it's going to be hand-delivered, then it's to "Friend and Partner/Spouse".
I have never written cards for DP's family and friends from us both. I made that mistake with my exDP, and resolved that I was never doing that again. I buy the cards, and he knows where they are if he wants to write them to his parents, siblings and friends, but there is no way on this earth I'm writing them for him. DP and I sort of work together, so I write all our work ones and that's quite enough, thank you! 