To be honest, when I saw those Christmas pictures, one of the first things I thought of was that maybe chuckie told Tayler that if he was going to pay to have pictures taken, that he might of well take some with the kids too. Maybe that's why there isn't a family photo? (Unless there is one).
And I don't get why it's so hard for Tayler to quickly explain that she and chuckie aren't together, she can just say that they're getting along better and that he's only around because he wants to be with the kids. She can post 100 different versions of the day she held deaths hand, but can't make one post explaining about her and chuckie. After all, lying is what she's best at.