I haven't tried this myself in GMS2 yet, but I'd be interested to hear how this pans out...
I'm aware there are some Windows games (not of GMS origin) where this same issue is (or was) present (requiring a double-tap in order to register a left-click on Windows touch devices).
Some of those games were since patched to fix the issue, presumably as ownership of Windows-based tablets etc. increased.
Maybe there's some "gotcha" or weirdness in the relevant API/somewhere that's causing the same issue to crop up, potentially with various engines (or native code), not just GMS.
Something with the way you need to handle a "touch" event vs. a "click".
I remember "FTL" had(still has?) this issue, and here's a similar discussion, mentioning both "Darkest Dungeon" & "Banished" as having the issue some time ago...
https://www.reddit.com/r/gamemaker/comments/4ilvlo/touchscreen_issue_single_click_single_touch/
...I'm sure there are plenty more.
I remember spending some fiddling with Windows touch settings, eg. turning off "hold to right click" and similar, but no joy there.
Anyway, given that it's been fixed in some of those other non-GMS games, it should hopefully be something that's fixable here too.
The "terrible performance" thing sounds more serious... possibly related though?
EDIT: Actually, I'm now remembering more clearly... the specific issue with those other games was that, when you perform the 2nd "tap", the game would then register as if you had "clicked" at the point on the screen where you made the 1st "tap". As if API/game had only registered a "mouse button pressed" event on the 1st tap, and was waiting for a "mouse button released" which came from the 2nd tap, but then took the screen coord from the 1st event. Does that sound like how it works in GMS2?