In the pentesting community everyone carries a tool called a relay bridge on their keychains. It is simply a piece of wire used to bridge across two electrical points. Inside the gate control box (which is usually keyed alike to thousands of others across the country, that use a common key), there is usually a single relay that controls the opening of the gate, the last component going from the low voltage RX circuitry to the high voltage motor or actuator. Simply bridging this relay gets the gate to open.
So despite all the effort they put into high security fobs and RFID badges, often the easiest vector of attack is to just ignore those.
That is one option- Simply supplement the existing RF circuitry with a second set of your own design, that both activate the final relay.
But I also like 6v6gt's solution. Use one of the existing transmitters as a stationary relay station, and electrically connect your preferred brand of transmitter to its button, thereby extending its range.
A company called Linx Technologies used to make these high power rf amplifier chips, that would boost the 433MHz signal significantly past the legal limit. Unfortunately they discontinued those, but they do still sell all kinds of RF chips made for remote control, some of which offer encryption options, if you are down to engineer a remote system yourself. They also sell prefabricated remotes that pair up with their receiver chips.
Personally I would also add networked connectivity with an esp8266 so I could open it from my phone as well, assuming you can find a spot to mount the original remote that is close enough to the gate as well as a wifi signal.