There should be a 4 wire RS485 communications plug on the main board of the AquaRite on the upper right of the board. They are little snap in plugs with 4 screws that you insert the wire into. See this picture:
https://idoneitmyself.files.wordpress.com/2010/11/img_1991.jpg
There should be (2) 4 wire communications plugs on the intellitouch board (labeled J7 and J8).
Run a 4 wire connector from the aquarite plug to one of the intellitouch plugs. Then activate in the control panel as shown in the manual. Wire 1-4, 2-3, 3-2 and 4-1.
Double check instructions with Pentair and Hayward to verify. Have software revision information handy.
Only you can decide if you are comfortable doing this, but I suspect that you can do it.
Pentair colors: 1 black,2 Green, 3 Yellow, 4 red
Hayward colors: 1 red, 2 black, 3 yellow, 4 green
https://www.hayward-pool.com/pdf/manuals/AquaRite&AquaRiteXL.pdf
http://www.pentairpool.com/pdfs/intellitouchcontrolsysUG.pdf
http://www.pentairpool.com/pdfs/IntelliTouchOM.pdf
http://www.pentairpool.com/pdfs/LoadCenterIG.pdf
Alternatively, you can just wire the power to the AquaRite to the load side of the pump relay and control the AquaRite from the AquaRite box.
In any case, don’t do anything that you’re not comfortable doing.
If you want to post pictures as you proceed, that could help us better advise.