A/C fan comes on when heater is on
Have you checked the air conditioner controls, if you have any? Yours may not have seperate ones other than on the thermostat, as many now do not. But if it does have, make sure that they are turned off. If you don't have any controls but the thermostat, check to see if the a/c is blowing cold air, at the same time as the furnace is operating. If it is, there is no doubt that the thermostat is the problem.
You don't say what make of a/c you have, but if it is a Dometic the actual controls for the furnace and the a/c are both located in the a/c unit. With mine where we have only the thermostat to control either the furnace or the a/c, there are three switches on the thermostat. One selects (top to bottom) cool, off, and furnace. The second is labeled Fan and has positions on & Auto. The last switch has no label but has positions high & low and it controls the fan speed for the a/c unit. Now if you have the same as mine, or another make but with the same type of control, there are two things that could cause the heat and the a/c to come on together. The most likely is the thermostat, but the control board in the a/c unit could also do the same thing, as it is where either the a/c or the furnace seems to be controled. With the furnace in operation, there is an audible click at the a/c unit when the heat comes on and again when it goes off. I'm not sure why, as I have never traced out the controls, but I can assure you that it happens. I guess that I should look into that before I have some problem as I just looked and the third addition RV Repair manual from TL books doesn't have this type of control in it either.
Hmmmmmmmm?