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I have a gps device that can cut off the petrol pump electric line. I want to add another relay in parallel with the one shown in the picture to cut off the electric line of the LPG valve, the question is, does adding a new relay add more load that may harm the gps device?.

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcT7EnoqDaz66SH45k5-hjKZZivrCub7ajzkQg&usqp=CAU

Difficult to say. When the circuit try to draw too much current from a source, the voltage delivered by the source may drop (internal resistance model). So, if two points A and B are initially such that Vab = Va-Vb = 3 volt, there may be cases where Va drops much more than Vb (alimented by another source, as example) and Vab becomes -3 volt. Any device sensible to voltage reversal may then be damaged. That may happen to I/O pins of some MCU which are designed to accept only positive voltage, as example.

In multiple parallel paths, it is also possible that one of the path closes (a transistor changed its behavior because of the voltage drop, and closes one of the paths), which creates a momentary excessive current in another branch. Current rush can also be a problem for some systems (current at startup or at some device getting active).

Without the datasheet of your gps device, about the amount of current it can deliver, no one can really say, I am afraid.

My solution is to have one relay connected to the gps device witch in turn switches on and off two other relays one for petrol pump and the other for the lpg valve. Is this method better (safer) ?.

Doing so, I don't see any problem for your gps device.