Looks okay but,no need to ground to batt. I would use a GOOD body ground. You'll find plenty under the hood since you already have the wire there. Now as far as powering the relay you can do it one or two ways.
1. Run a branch off your pos batt cable to the pos terminal on your relay. Now run a wire from the grd(-) to a switch and then to a good ground. Now u flip the switch and the inverter comes on.
2. Go your orig route and wire BOTH the switch and the inverter.
Also I am new but, through ALOT of reading crank up before comp on.