But I want to switch it and wire the red ceiling wire to the black fan wire and the black ceiling wire to the black/white fan wire so that the particular switches work the way I want them to. Is this ok, to switch them?
Black wire on the fan is for the fan motor, red wire in the fan is for the light, the white wire is the neutral wire. So if you do want to switch the light off and on you have to tie red wire to the switch and the black wire can be tied to the hot at the ceiling box so you can control the fan with the chain only. If you have one switch leg in your circuit then you cannot do anything but switch them both if you tie them together. I think I am understanding what you are saying here. White Alyse ties to white Black is for the fan motor and the red is for the light. If you have three wires in the switch then you can tie them the same way color to color. Hope this has not confused you You can email me if you need further help