I have a 1989 mobile home with a coleman air handler that runs and it will blow cool air when on cool and warm air when on heat but it seems to blow both at the same time so that it never gets truly cold or hot. We had an ac guy come out to service the unit but he said he couldn't service with it running heating and cooling at the same time. He said it could be the thermostat or need a new inside unit. We replaced the thermostat and we have the same issue but I am was wondering if it could be a relay or something with the wiring that we could check first as a unit is rather expensive.

Since you didn`t say wheather the furnace was electric or gas,its going to be just a guess. I`m going to assume it is a electric furnace, the sequenser is kind of a relay of sorts that could and many times is the cause of this happening, look on your wiring diagram or the legand diagram and it should lead you to the sequenser and test with a meter