Finally i found the time to fix my button. As expected, the button daughterboard was able to shift its position, and because of that the outside button sometimes missed the electrical button.
I wonder if something was missing in my watch, because i haven't found anything that would have held the button in position... In the end i glued a bit of plastic foam to the button, so that the display presses the button into position.
Because opening the watch was a bit challenging, here is a little howto: Disassembling of the bangle 2 display.
As stated, the display glass must be heatet to not much above 80° using ho air. I used hot air of 100°, first with some distance to the watch. I then checked the temperature of the glass surface from time to time using an infrared thermometer, reduced the distance step by step and tried to remove the display using a suction cup. When the glass surface reached 83°, the display started moving a bit when pulling. Here i kept the distance and repeated heating/pulling until the display glass came free.
Tipp: The display was glued in place with liquid glue that has hardened in the meantime. If the display has come loose at one point, it will not stick there again when you press on the display.
Tipp: The display will tell you its temperature by itself. At ~70° the display content starts fading away, at ~80° the display content has completely vanished.
To reassemble the display, i used standard double sided adhesive tape. I fear this is far less solid than the original glue, but makes service easier :-). I will report back if the display falls out at any point.