So I think it is probably also confusing to the WS. On one hand you are sending him pictures or in Ginger's case playing MarioKart so everyone thinks everything is cool with blended families. If they didn't think it was cool, I guarantee you it would be "I" thank you instead of "we".
It's totally cool to do the blended family thing if you think it's best for your kids but it is totally ok to teach your kids about boundaries too.