Are you smiling or are you in pain?

As you will know if you have been reading my blog for awhile my daughter is on the Autism spectrum. I'm reminding you of this because I am hoping someone can offer some advice about taking pictures of children on the spectrum. Any time I mention pictures my daughter starts giving me attitude. She doesn't want anything to do with having her picture taken. Even when she cooperates it is a struggle. She looks like she is in pain when she smiles. It takes many do overs to get a picture that doesn't look rigid.

This past weekend we took some fall pictures while we were out enjoying the changing leaves. I know we took over 500 pictures and ended up with less than ten that looked natural. I tried to get her to think about things she loves like her cats. I tried catching her off guard. When she spots the camera she gets that rigid, uncomfortable look.
Here are a few examples.

How can I teach her to smile naturally without looking so frigid? I showed her the pictures and tried to get her to see the difference but she doesn't understand what I want. I want to have some pictures to be able to look back upon someday. I only do pictures a few times a year because they are frustrating for everyone. Any advice is gladly appreciated.
Here is one of the pictures that turned out great.