Thanks.
I think I have got some clues. Ubertooth One would be a nice thing to have, but it costs quite a bit (in addition to HackRF that I already have).
I think I will try NRF24LU1 to start with. Maybe it will catch the signal differently. Those RF dongles that receive the signal from the remote control are really small to be able to do many manipulations, and they all work really good. Very rarely happens that a press of the button will not go through. So, there must be something that could filter out most of the noise. would that be the exact frequency, sending sync on several channels. i guess I will have to figure that out.