The first column shows the past/current situation, the second column is the answer, and the third column gives extra details.
Book + Man - a secretive man. Well, that would be my Dear One. Although he decided he wanted to invite his family (including aunts, uncles and cousins) over to ours for the 25th, he doesn't actually have all that much contact with them, so it may well be a bit stilted.
Ship + Anchor - a foreigner's homebase and/or a trip that brings stability. Here I see my mother: she is a foreigner, but our house has become homebase for Christmas since Big Boy, her only grandchild, was born. Particularly as, being European, we normally celebrate on the 24th anyway. Also, I have been worried about asking her to travel to ours on both the 24th and the 25th. This suggests, though, that if the trip brings a feeling of stability it may still be welcomed.
Park + House - a family party. This says that having my mum and stepdad over separately on the 24th will feel much more festive and also more of a true "family affair" than the time with DO's family.
So, based on this reading, I will ask. After all, she can always say no if it doesn't suit them, but I think we'd all enjoy it if they did come.