You might try redoing your description of what the issue is.
The air conditioner should not operate if not on shore power. Are you saying it does??
With the fan set to auto, and plugged into shore power (electric), the AC fan should not come on, when stat is set to heat. If on low, or high fan setting, then both may operate.
If it used to work as I described, but now does not, you may need a new stat.
Jerry