I have questions for you and some suggestions. The pics are great so far.

1) How big are the pool and spa?
2) How many BTUs is the heater?
3) How many HP is the Northstar pump?
4) And the Blower?
5) How many jets in the spa?
6) How many pool returns? Any in the spa?
Assuming the heater is functioning correctly, except for the remote function, most 8' spas take about 20 minutes to heat up.

If the tan wire is not broken, then turn on the heater and then press and hold the mode, temp up and temp down buttons simultaneously. That will put your heater into remote operation mode. If the spa doesn't reach the desired temp, repeat the above procedure, turn the temp on the heater to 103 degrees, then put it back in remote mode. If it still doesn't reach the desired temp, the water temp sensor may be dying.

The skimmer lines are on the wrong side of the 3 way valve. I would move them over to the same side as the pool drain and replumb the pool suction lines in one port of a 3 way valve and the spa suction on the other. The 3rd port goes to the pump. Put the valve actuator on that 3 way. You won't have to manually turn valves anymore.

Are there no lights in the pool? If there are, you can also add a relay to control them.

A hard wired full function controller can be added in the house to resolve the remote's loss of communication. Ill bet it's too many walls or distance causing the interference. The slow response is typical for Jandy wireless remotes.

The Pentair Quad DE is the easiest to clean. While it can be directly plumbed, I prefer the added functionality of the optional multiport.

We can answer more when you answer my questions to you.

You have your pool and spa return pipes marked wrong.
I agree with poolguynj about pipe orientation.
You should replumb your suction and return to take advantage of remoting the current valve actuation for pool or spa.
You could leave the piping in the same manner and purchase an actuator for the pool main drain. Put it on solar using the remote to close it when you turn on the spa.
If you have a PS-4 you could then tie your pool and spa light switch legs together and put them on the controller too.
aux 1 would be cleaner
aux 2 would be blower
aux 3 would be pool/spa lights
aux 4 would be close pool main drain

I'm curious do you have a wall mount remote in the house or do you have a radio hand held remote and is your system PS-4 or PS-6?

See ya,
Kelly