I sympathize but do you really know the Mom told the girls they are going to get fat? Your step-daughter is 13 and at that age they are very self-conscious. We eat healthy and exercise, but my 15 year old (who is thin but not anorexic) is always saying she is fat. I have never ever said anything like that, but the thought remains.
Also a 13 year old may be dieting on her own, and may be using the "Mom told me to do it routine". Thirteen year olds do not have the skills to confront an adult, so it is easier to have a scapegoat. She is not really lying per se, she is just 13.
Since the 13 year old lives mostly with her mother, then on the days you have her DON'T have pizza. You really should not have pizza at all if you are living a healthy life style. That particular food should be listed on the once or twice a year treat list.
I also do not see any mention of exercise for you, your spouse or your step-children. You state that you are "My 16 year old doesn't have as much of a problem with it because she is older and I am constantly trying to tell her that if we eat right and constantly doing things like we have been, so won't have to worry about it". That is just as bad. You should not be discussing this if it is a passive way of contradicting the Ex.
You, your spouse and his Ex are ALL working against each other.
What does you step daughter's Dr. say? Are they concerned about the weight. Is there a family history with your spouses family?
You state that the girls are no where near chunky. Sometimes when a person is overweight, they are unable to judge if someone else is chunky or not. (I have been there, done that.
The Mom, you (and presumably your spouse - although from your description he seems a passive bystander thast is letting you do the heavy lifting on unpleasant subjects).
Both sides want what is best for the kids, but both have radically differenct ideas of how to accomplish that. You are not a monster and neither is the Ex. (remember, everything you know about the ex is filtered through your spouse).
It is best to leave this alone. Once you both stop butting heads and digging your heels in, things will lighten up for both sides.
REally the girls will only be there a short amount of time when you consider the big picture. They will make their own eating and exercising decisions.
Prepare healthy meals and exercise with the kids. The Ex can only drive you crazy if you let her.