Hey Tim,
there is an IB school here that has about 50% chinese content called the Chinese
International School (CNIS). Am not sure if your daughter will be in Grade 6 or Grade 7. If you look thru the posts on the school, it has mixed reviews, I think more bad gets written than the good. Considering you are only looking for a semester, I presume it should be ok.
I don't know much about Grade 7 in that school but up to grade 6, the Chinese nationals that send their kids here are very pleased with the school, the chinese is on par with the schools back in Beijing and because of the small size of the school you get alot of one on one esp for language.
The school from grade 1 onwards splits the kids into 3 grades of chinese class, if you have no chinese at all, if you have some and if you can speak chinese or have a parent that is chinese that can help you at home.
I have kids there and I think they are thriving, though if my kids could go to a school with higher chinese content, I would send them there (it is the school with the most chinese content in singapore).
As for moving here and visa's... I guess a semester should be easy ie you may have to travel in an out or make a special request, I think your daughter should have no problem with the application of a student visa and the school is v helpful in applying it, your wife should have no problem also as the "accompanying parent", you I am not sure, u may just have to do the travel in and out ev 2 weeks....
I have another suggestion for you though, I visited schools in Beijing and there is a wonderful-wonderful small one called Daystar, it is up to grade 6 only and it is half montesorri and half chinese curriculum. The staff and admin are very switched on and the school is very well organised. I could go on and on...
Maybe that could be an option for a semester abroad? they are out in Shunyi (near the airport) tho and not in the city.
Or if you guys are very flexible a semester is not a big deal in your child's overall education as opposed to the experience, you may consider doing a semester where she is originally from? there is a good tour group that may be able to help you in organising something locally for a semester incl schools though of course you may not have
International Schools in the non-beijing, shanghai or guangzhou area. The tour group is called Lotus Tours. They are organising our summer semester for the kids in Guilin.
PM me if you want more info on any of the above.