Is there a way to play multiplayer in Minecraft Java Edition? Not splitscreen or joining servers and realms, just two people in a world?

I'm sorry to state that Minecraft: Java Edition requires either an online server or all players on the same network (LAN) for multiplayer. Since you & your sister are located in two separate states & time zones, you can't utilize the LAN connection without using Hamachi or similar virtual LAN tunneling services.

It would be easier for one of you to start up your own private server for both of you to enjoy. If you're unable (or more likely, unwilling) to set up your own private server, you may want to consider getting a Realm subscription to offload the server operations to Mojang. I know it's not your desired option, but it has WAY LESS HEADACHES than the alternatives.

Nope. There's no way to split the keyboard for 2 controls. Even though you can connect a controller, computer wise, it doesn't matter.