I have two wall switches. One controls my ceiling fan and one controls my light. I would like to add a remote into the mix. Ultimately I would like to control my light and fan using both the wall switches and the remote. I want to keep the wall switches hard wired (I.e., not smart switches or wireless). Is this possible?
Lutron has an answer to your question
As it turns out, Lutron, at the time of this writing, has just introduced a fan control into their line of Caseta wallbox/remote capable controls. I would use two Caseta controls side by side; namely, a PD-FSQN and a PD-5NE. Note that they both require a neutral wire at the switch box to work (which may or may not be an issue with your wiring, we'd need photos of the inside of the switch box to know for sure), and rely on wall-mounting hand-held remotes (Caseta controls use Lutron Pico remotes) for multi-way control, if that is acceptable for your application.
No. You can't mix-and-match different control methods. because one of them has to be in charge of doing the actual controlling, and so the other one needs to speak its language.
The only way that works is if engineering staff has burned the midnight oil doing the technical things necessary for them to share protocols etc.
Smart-home technology is becoming the "universal solvent" for this stuff. For instance, you can get a "smart switch" style fan controller + lamp dimmer that controls a conventionally controlled fan, and either sits in a module in the fan rose, or is mounted at the switch location (where it has controls). Then, use an app on your phone for the remote.
With-fan remotes have one purpose, and that is to make the fan cheaper. In that sense they are very low-rent - used on the cheapest fans, which includes most fans from the big-box stores. Cheap fans don't get extra features to allow you to increase their versatility like that. Actually, the remotes are flimsy and will likely fail long before the fan does, leaving you scrambling to find a remote from a defunct fan manufacturer. If it's a "house brand" fan from a local big-box store, forget it: this year the supplier is Dees Ees Chunk Export Co. Ltd., and 3 years hence it'll be Wee Low Bydd Fabricators. Naturally their remotes won't talk to each other, and you will be expected to simply trash it and buy another fan.
The Hunter wireless fan control would work with simple on-off wall switches. The receiver placed in the fan shroud gets a wireless signal from a battery powered remote. There is one button on the remote for the light which allows dimming. There are four buttons for the fan: off, low med, high.
The output of the receiver would then go through each wall switch which would allow the fan and lights to be turned off at the wall. If the wall switches are on, then the remote would control the fans and lights.
The Hunter remote does not require a neutral in the switch box. It was designed to allow a ceiling light controlled by a single wall switch without a neutral in the switch box. There is a plastic caddy for the remote which mounts to the wall switch in such a way that the wall switch can be operated with the remote taken off. This caddy could be mounted directly to the wall.