Hi Jules,
I’m happy to help you out with this and to assure you … you’re not alone in your confusion. 
Short answer here is all three are UNNECESSARY for our controller. This should make you life a bit easier.
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It appears your current (Hunter Pro-C) timer required a hard-wired power source. That’s what the AC1 & AC2 are for. It would be a good idea to cut all power to the unit - from the breaker - before disconnect. Insulate those wires in case they ever go “hot” and set aside. For our controllers, power is provided from a wall outlet and is plugged directly into the unit:
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The REM wire is for a remote. Also unnecessary, as you’ll be controlling your new Gen2 from our app!
Speaking of the app - since it appears you have a Master Valve (or Pump), remember to enable that setting when you configure your new controller (From the Dashboard screen > Device Settings > Advanced > Master Valve Toggle)
Happy installing, and feel free to reach out with any further questions.
~Lucas V-K