"So if we built 100 million houses the price would still go up due to the trade imbalance?"
If you could somehow manage to build 100 million houses without effecting any other variable then the prices would certainly go down.
That doesn't change the fact the simple supply and demand relationship does not correctly predict the housing market because other variables also play a role. For example when interest rates are low people think they can afford more house or to pay more for the same house.
But Chinese exchange rates and trade effect interest rates and inflation. Oil prices also effect inflation. There are also psychological factors and substitution issues.
It's pretty darn complex to predict housing prices even one year out. If you could do it reliably you could make a lot of money.
I'm just a lowly engineer, myself, but I'd just like to point out: what you are talking about are indirect factors, i.e., things that drive demand or supply. If demand is high - regardless why, e.g. low interest rates - and supply is low - regardless why, e.g. development regulations - I'd bet my right nut that prices will rise. But I'm not an economist, so what do I know...