There isn't an "open" button that comes up to open a chest minecart. It was there in version 0.15, but nothing comes up when I move my finger over the chest minecart in 0.16 and I just updated to 0.16.1 to see if it was fixed and it's still not there. So there is no way to open the chest minecart. I even destroyed the chest minecart and recreated it and it still didn't give me the open button. I tried this on my ipad air 2 with mcpe 0.16.1 and my iphone 6s+ with mcpe 0.16 and it was the same on both.