There are systems both wired and wireless designed for Motorcyclers and at least ONE wireless system for RVers that use a system called VOX. (Voice Operated X-Mit) These are Simplex (Single frequency) devices most operate in the FRS or GMRS band.. They do not require you push a button but generally the first syllable may be lost when you talk (SOUND keys the transmitter) and of course only one can talk at a time.
As a Ham Radio operator I have worked Duplex many times (Two frequencies) and depending on where I am full duplex (Where you can cut in while I'm talking) is possible. In fact when I was working MY radio (The Dispatcher's radio) was full duplex.. Car radios are not.
The Technician license is a good option.. Or you could simply use FOUR FRS radios.
But the RV-Headset would be what I'd recommend for you.