My daughter has been at the Dallas International School as a full-time student for six years. It wasn't until year 4 that she would start to speak French and that is after getting instruction in French everyday for most of the school day. She can read, speak and write it, but is still far from fluent, but she could get by in a French-speaking country if needed.
She gets just an hour or two of Spanish each week and while she has picked up a few words, she would never be able to carry a conversation with a Spanish speaker. She can read Spanish, but doesn't comprehend it like she does French. Her Spanish teacher this year is excellent...really pushing the kids to learn in a fun way in the short time she has with the kids. But in order for my daughter to learn Spanish the way she has learned French, it will take a lot more immersion in the language.
I took French from age 11 through college. I did well in class and thought I knew the language. Got to France for my junior year and had no idea what people were saying. Too much time was spent on reading and writing and not enough on oral acquisition of the language.
I suggest doing a combination of instruction at any of the schools you mentioned and also finding a babysitter or playmates for your kids who speak Spanish and agree to only speak Spanish with them. It will not be easy for the kids at first, but if you stick with it, they will adapt. Find Spanish language TV programs for the kids to watch during TV time. The school/camp instruction is a good start, but to get them fluent, find ways to immerse them in the language on a regular basis that aren't instruction-based.