If cost is a primary concern, the kids can go to local school (just like Chinese kids who come to the US). The expat continuum goes from 'bubble' to 'going native'. Bubble is most expensive. Might as well stay home, no?
It is also legal for expats to home school their kids (not legal for the locals).
There is a strong sense of entitlement present in American culture which leads to unrealistic expectations when living abroad. This manifests as the so-called 'ugly American'. China is a place where 'zero-tolerance' is literally a foreign concept, and anything is possible with persistence (and good connections). Which also implies the downside -- nothing is permanent or guaranteed, either.