I’m no expert on the implementation of my.openhab so this is largely a guess on how I think it works based on observation.
I do not think that having multiple OH servers on the same my.openhab account was ever an anticipated use case. From the documentation and my experience there is nothing that would make me think it would work. It makes sense that your Items from both instances are showing up because that is a data push (i.e. your two OH instances are pushing the data to my.openhab). But anything else I would not expect to work because I doubt the work necessary to keep track of which instance has what Items or sitemap is in place. And even if it was able to do that, there is all sorts of complexity added in dealing with duplicated names and such.
So I think the short answer is that is not supported. If you want to have a single sitemap you can try to link the two Event Buses over MQTT (see the MQTT Binding page for details).
That’s what I suspected. I have worked around the problem by creating one my.openhab account per site, but that creates its own set of challenges on the client side (not well supported by browser, android app…). I have seen that there is an enhancement request for this for the android app, but no plan as such. I’m looking at ways of having two app instances on Android…
Have you looked at some of the other third party apps like 3House? Then you could use Habdroid for one and 3House for the other. Its not ideal but it can get you by until a better solution comes along.
As far as I can tell tell 3Hou.se does not support my.openhab.
I have managed to rebuild the openhab Android app with a different name (I even have a different color icon!) so that I can have two openhab apps with different configurations. A bit of a hack I give you that, but it serves my purpose. If I have more time I could try to help integrate something in the official app.
MQTT seems to require a broker, and openhab only provides a client, so it looked a little convoluted, but one day I would like to look into it some more.