I'd love this to be discussed more often - the game handles mobile hotspots really badly!
It sounds like you are having the same experience I have when I play by mobile hotspot on PC with mediocre internet (enough to stream a video or play most online games, but not well) - it can take many attempts to log in from the character select screen, and if you get in you can play well in that zone, but changing zones is likely to "loose lobby connection".
I have 1 workaround that definitely works, one that I think works but is anecdotal, and one that works for me on PC
If you can travel to another player (e.g. through guild) then you have an excellent chance of successfully changing zone. I've tested this, and I think this suggests the problem is that the game struggles to choose your instance of the zone when there is a questionable internet connection.
I believe, but cannot properly test, if you can stay in a zone for a while, then you are more likely to stay in the game. This might be a "false positive" of playing when the intermittent internet got more stable, but waiting a while, or moving around one zone seems to increase the chance of changing zones and having a good play session.
Finally, on PC, I have stadia as well as the standard edition - you have no problems loading in or changing zone on stadia as long as you have enough internet to load it up. Sometimes I use stadia just to change zones successfully, then I log out of stadia and back in through the normal PC client.
I travel for work, and the main reason I take breaks from ESO is frustration with how it copes with my mobile hotspot in less ideal places... I get that my internet is my problem, but it can take 10 attempts to log in, and then it works fine, so I don't think it is just my internet that is the problem.