What is your son allergic to? You said he couldn't eat anything they sell in a movie theater. You also said he can't go to parties at a pizza place, or the Japanese restaurant.
Did the mom really call you up to ask why your son didn't eat anything at the movies? I don't know why she would care.
And, where do you live where 12 year old boys are only having parties at restaurants, with no activities at all---just eat and leave? I don't know any boys---or kids--- (except maybe older, drinking-aged one's) who would plan a birthday 'party' like that. I'm wondering... can't your son at least go for the social aspect of it at least? Most kids love shooting the breeze with each other. I would think if he was close to any of these boys, he would want to be around them, even if he can't eat the food being served (can he eat beforehand, as a PP suggested?). Sounds like maybe he just doesn't care to go.
As for your daughter's friends: I'm not Mormon, but I've never heard of a service being that crazy. Why does your DD hang around with these people who have no respect for her wishes? If she has repeatedly told these 'friends' she doesn't want to go to church with them, and they keep bugging her weekly to go, she should either be more aggressive and say "NO, and please do not ask again", or find some friends who are more respectful.
As for teaching the kids to lie....
There are alternatives to how you are approaching your situations. It doesn't have to be one extreme or the other, really.
Did the mom really call you up to ask why your son didn't eat anything at the movies? I don't know why she would care.
And, where do you live where 12 year old boys are only having parties at restaurants, with no activities at all---just eat and leave? I don't know any boys---or kids--- (except maybe older, drinking-aged one's) who would plan a birthday 'party' like that. I'm wondering... can't your son at least go for the social aspect of it at least? Most kids love shooting the breeze with each other. I would think if he was close to any of these boys, he would want to be around them, even if he can't eat the food being served (can he eat beforehand, as a PP suggested?). Sounds like maybe he just doesn't care to go.
As for your daughter's friends: I'm not Mormon, but I've never heard of a service being that crazy. Why does your DD hang around with these people who have no respect for her wishes? If she has repeatedly told these 'friends' she doesn't want to go to church with them, and they keep bugging her weekly to go, she should either be more aggressive and say "NO, and please do not ask again", or find some friends who are more respectful.
As for teaching the kids to lie....

There are alternatives to how you are approaching your situations. It doesn't have to be one extreme or the other, really.