It's extremely frustrating to win a city just to lose it the next turn because the army is outside of the city limits. Can this be fixed please?

Yes, agree here.

Currently, it's one of those race on the next turn to have your unit move in.

A weird one happened to me where I won a city, then a third AI who was also at war with them instantly took the city because it was now undefended (and I couldn't move into). I could no longer attack it that turn, because it says you can only "win" the city one time per turn.

Hard yes!

I don't get this; how can your army that conquered a city be left out of city boundaries next turn? Your army should have been next to the city walls to besiege and capture the city in the first place. When your enemy try to besiege (now your) city that army of yours should be close enough to reinforce defending or sortie. 

Dayvit78 wrote:

A weird one happened to me where I won a city, then a third AI who was also at war with them instantly took the city because it was now undefended (and I couldn't move into). I could no longer attack it that turn, because it says you can only "win" the city one time per turn.

That's really weird. Did third AI declare war on you or were already at war with you? They shouldn't be able to attack a city you just conquered, since it technically becomes your city as soon as you capture it.

In theory it should be a simple problem to solve, just at the end of a conflict that captured a city, the units are automatically transferred to the administrative center of the city

Atens7 wrote:

In theory it should be a simple problem to solve, just at the end of a conflict that captured a city, the units are automatically transferred to the administrative center of the city

This. Thank you.