How to access automatic gates (radio + gsm)?

Question

Do it yourself

There are automatic gates that open either with a radio remote control or by a call from a list of numbers specified in the controller. At the moment there is access from my phone number, it is necessary to ensure the possibility of opening for family members (now they call me to call this gate).
1. A company servicing gate automation breaks exorbitant prices for additional key fobs (2500 rubles).
2. There is no access to the controller, there are no free places for rooms either. It is authentically known that some of the numbers are dead.
The question, in fact, is how to secure access to the yard with little bloodshed.
A practical solution has been found.
Now I would like to see options from the series “we are not looking for easy ways”:

• Write a program for android that, upon receiving an SMS with a certain text from the wife's number, would make a call to the controller to open the gate. (minus: long delay between sending SMS and opening the gate)
  
• Solder shit with a gsm module that would do the same thing autonomously using AT commands. (minus: you have to sacrifice a sim card)
  
• Stand with a radio at the gate and try to record the remote control signal, then record it on a universal or homemade remote control (minus: I don’t have such a receiver)
  

Please do not think that I suffer from bullshit. The humanities want to come up with and implement a practical task, because they are tired of writing tic-tac-toe in python and blinking diodes on arduino.

Answer 1

Automation manufacturer? Is there an open button?
New remotes are registered through existing ones or, alternatively, you can make a copy of your remote to a universal one.

Answer 2

What about call forwarding?
for example, everyone who calls number A gets to number B, while B "thinks" that number A called.
I know for sure that you can call from Skype so that my number is displayed.
Thus, you take a new line, unknown to anyone, you score in the slot instead of your own, and only the family knows this number ...

Answer 3

Thanks for the good advice. Unfortunately, experiments are not possible at the moment - some kind person who does not read the Toaster broke something and the gates have been open for more than a week.