Where does the remote sending unit actually install and fit inside the fan?

It fits inside the canopy. If you are having trouble getting it to fit in the canopy, there is a thread somewhere on these forums explaining how exactly it lines up in there.

Light will not turn off. With the remote

We have a Hampton Bay 44 inch Carriage House II ceiling fan to install on a flat ceiling, however the remote control does not fit above the fan (not enough room). We were told there is only one remote control for these fans. How can we install the remote?

The SENDING unit is the one with the buttons, the RECEIVING unit goes in the fan canopy.

The receiving unit does not fit into the fan canopy.

datasleuth-you pigtailed on another question and I was answering that one. Post your question separately to avoid confusion.