i feel badly for you. i apologise for some of the difficulties you have had with my profession. its embarassing.
okay here we go...
1) how could there be such a big difference in rx between the 2 doctors? the main reason is b/c this is an art, not a science. patients think that they have some rx in their eyes and we eye docs measure that rx and its a hard, repeatable science. truth is every person has a "range" that they see well thru, and if you went to 5 different eye docs you'd get 5 slightly different rx's. no one would be way off, but its also doubtful that any of them would be identical. there is about 1D difference between those two rx's in the right eye and about 1.5D difference in the left.
2) how could there be a difference in the actual rx as measured by the PO and the optical shop? well there are a bunch of possibilities, and i bet there is some sort of combination going on. there could be differences in the equipment used to measure the rx, and differences in user technique used to measure the rx. plus there is the
conversionConversion disorder factor...one rx is in "minus-cyl" form but the PO rx is in "plus cyl" form... to be honest i dont know why the rx's dont match but you're right, someone is incorrect.
3) which rx should you choose for your daughter? its sad to me that you feel like you have to choose. but i'm going to give you my opinion: in general in most young hyperopic patients, especially those who are esotropic which i ASSUME your daughter is (one or both eyes point IN)...the more powerful rx is probably the safer one. if the more powerful one was incorrect and overcorrected her making her distance vision blurry its really not that big of a deal. however if the less powerful one was incorrect and she was still undercorrected and ESO (turned in) even with the glasses on, that *is* a big deal. i'll take distance vision blur in a pediatric patient over constant esotropia EVERY TIME. every single time.
as for how to get your daughter to wear them...its really, really difficult. i'm sorry but you have to be mean. FORCE her to wear them. this is a big deal. she could permanently lose vision if she hasnt already. plus when she gets school age (i forget how old you said she was) she will have a VERY difficult time if you dont hash this out before then.
good luck. wouldnt hurt to get a *3rd* opinion...