Hello and good afternoon,
Thank you for allowing me to assist you, my name is Joe and I will be happy to assist you with your concern today.
Generally speaking this is usually related to a harness/connection that is bad such as corrosion which is a known problem on the harness going under the seat and dash, a ecu harness or the ecu itself.
The remote start wiring should not effect transmission as much as a no start condition for example.
Check the harnesses/wiring under the dash for loose connectors, loose pins in them, corrosion, etc.
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