Now, whether or not Kate, Mike, and Autumn were invited the year they were engaged we can’t actually say... we know none of them attended Christmas at Sandringham, but we don’t know that they didn’t have the option. T Cambridge, Tindalls, and Phillips don’t spend every Christmas at Sandringham, so it may just be that that year they chose not to. .
People who thinks Kate would be miffed should also keep in mind that William wasn't at Sandringham on Christmas 2010. If William's not there, I do think Kate would much prefer to spend Christmas with her own family.