For the coming festive season, our first here with you in America/the United States/the US, we wish you a Merry Christmas and a Happy New Year - with a couple of gurgles from our new baby (name).
from (wife's name) and Lackieu
This is if this is your first Christmas in USA and is meant for people in America. Choose whether you refer to the States as America, the US etc - just write one of them. It is a nice gesture to place your wife's name first.
For family and friends in Vietnam:
For the coming festive season, our first apart from you all, we wish you a Merry Christmas and a Happy New Year.
from (wife's name), Lackieu, and our new baby (name)
However, it might be cultural that the man's name come first in Vietnam.
Student or Learner