How to reverse-engineer a remote control?
First, find the FCC ID of the device. If they are wireless devices approved for use in the US, there should be an FCC ID somewhere (either on the device proper, or on a wireless module inside the device). Use the FCC ID Search to look up the device, this should tell you what frequency the device uses. Alternatively, the device might tell you what frequency it uses. Or, take a look at the ICs, and look up the part numbers of everything that looks important. If you're lucky, they use a common wireless SoC with a public datasheet.

Once you know the frequency, things get tricky. If the device operates in the 2.4GHz band, it could be pretty difficult to reverse-engineer it, because the protocol is likely non-trivial. In which case, your best bet would probably be to bodge the existing remote onto the Raspi (using the Raspi to "press" the buttons).

If they use 433MHz or 315MHz, it's possible/likely that they are simply using serial. If you have an existing receiver, you can try looking at the signal (analyzing serial on a scope is very easy, if you have a scope). Or, you could probe around on the transmitter board to find the TTL serial signal and capture that.

Pictures of the devices and their internals could help narrow it down, but that's the general answer.