3.3 V relay switches on/off/on - off fails 2nd switch off connected to Pi4
Your information about your circuit in the blue rectangle is very sparse, but I assume it is just representing the relay (note 1). If that is the case then you should expect problems because the rPi output cannot source more than 50mA according to this source and that would be at reduced voltage even.
The coil is specified at 25 Ohm and typical 3V, so this would require 120mA.
Now, why this manifest itself as you describe is not obvious, but first solve the drive problem (see below) and check if that does not solve the problem.
Bottom line - you will need a buffer of some kind between the coil and the GPIO output. A MOSFET or transistor is a very cheap and simple solution for this. There are plenty of design examples for such solution. Example here.
Note 1: If the rectangle you draw is the relay, then I don't understand why you need both Vcc and GND. You should use either one or the other to get active relay when output is low (use Vcc) or get active relay when output is high (use GND).
PS: a hand written drawing can be better than a poor digital drawing. Importance is the information is there - not the looks of it.