I think my reply below may be misplaced as rereading your post maybe your children are not youngsters. But in case they are I'll leave it as is (I lost a friend when young). If they're older then they won't think you've forgotten her. You can just add something like mum would have wanted me to wish you... or remembering my lovely wife/your wonderful mum 

Oh so tough... I feel for you. Heartfelt condolences. I do think putting your wife's name on the card would be a mistake. Your children might start to wonder if she's really gone. Or could be coming back. Especially at Christmas that's a difficult thought to have in your mind with all the supposed "magic" of it. And therefore sadly a seed best not to sow.By contrast sending a card from their mother written in advance of her death saying she had asked for it to be sent... well that's something else entirely. I think it would probably be best with just your wife's name on if so. And it would need to be clear that she knew she wouldn't be there for Christmas and is sorry she can only be there in their hearts now. I was unable to sleep at night for many years because I was told a best friend who died very young (age 11) had simply entered a long sleep. The idea of her being asleep was more terrifying than the idea of her dying or being differently "awake" in another world. But that other world has issues too when viewed from a child's perspective. If a child (or adult) thinks they can get to that other world what might ensue...Keep things simple. Don't be over-elaborate I guess.

I think my reply below may be misplaced as rereading your post maybe your children are not youngsters. But in case they are I'll leave it as is (I lost a friend when young). If they're older then they won't think you've forgotten her. You can just add something like mum would have wanted me to wish you... or remembering my lovely wife/your wonderful mum 

Oh so tough... I feel for you. Heartfelt condolences. I do think putting your wife's name on the card would be a mistake. Your children might start to wonder if she's really gone. Or could be coming back. Especially at Christmas that's a difficult thought to have in your mind with all the supposed "magic" of it. And therefore sadly a seed best not to sow.By contrast sending a card from their mother written in advance of her death saying she had asked for it to be sent... well that's something else entirely. I think it would probably be best with just your wife's name on if so. And it would need to be clear that she knew she wouldn't be there for Christmas and is sorry she can only be there in their hearts now. I was unable to sleep at night for many years because I was told a best friend who died very young (age 11) had simply entered a long sleep. The idea of her being asleep was more terrifying than the idea of her dying or being differently "awake" in another world. But that other world has issues too when viewed from a child's perspective. If a child (or adult) thinks they can get to that other world what might ensue...Keep things simple. Don't be over-elaborate I guess.