One outlet, two hots, one neutral, no power to the other outlets
Here is the probable answer: the “hot” white wire isn’t. It’s the neutral from your downstream outlets. It looks hot because you have something plugged in that is conducting voltage from its hot wire. If you unplug (or completely turn off) everything plugged into the non-working outlets, it should no longer appear hot.

Try connecting the two white wires together on the neutral side of the outlet.

In the future, always label wires before disconnecting if anything looks at all funny.