How is Ann's refusal to believe in Chris's afterlife existence affecting her and her family? How is she affecting the belief of her children?
The usual way. People involved shape each other. They define happiness, togetherness, loneliness, identity for each other at least in that they contain and reflect each other. (A more accessible example is the daughter's choice to take the shape of kindness: an Asian girl, in her father's representation.) And it's normative; as mirrors, they are the (only valid) means by which one judges oneself. And it's reciprocal; denying their existence not only equals (living) hell but keeps them incomplete and (their) heaven indeterminate. It affects them the usual way.
I'm not exactly sure how to answer this but I'll take a stab at it since this is one of my favorite movies and I've seen it several times.
How is Ann's refusal to believe in Chris's afterlife existence affecting her and her family? Well its affect on her is that she is stuck in Hell in an old house and in her mind she is living a dark reality (she doesn't know she is dead) and she will never again be reunited with her family.
So the affect on her family is of course sadness because they love her and want to be with her. They are also affected in that Chris decides to go after her and he is accompanied by (unknown until later) their son Ian who appears as Chris' colleague. Had Ian followed Chris into Hell to rescue Ann there would have been other possible consequences such as Ian become lost too.
How is she affecting the belief of her children?
Their belief in what exactly? In Chris' afterlife? I'm not sure she was affecting that at all. They both had already created their own worlds and Chris was in the process of creating his own. Had she remained in Hell I doubt they would have stopped believing in something they had first hand knowledge of.
If you're talking about their faith, I supposed the affect was that they were able to see how their parent's were truly soul mates which according to Ian is very rare, and how Chris was able to tap into that to bring Ann out of her depression and return with him to his afterlife.
Hopefully this provides some kind of answer. If not, you may want to be more specific in what exactly it is you are asking.