Only difference is the color. P4P v1 remotes can also be used on the other P4 models, changeable under advanced settings. Also the frequency can be changed between 5.8 and 2.4 which could cause your problems. Try switching to see if that corrects it, P4P usually uses 5.8 but in certain areas 2.4 might work better. Device must be connected to remote to make these changes but drone connection is not necessary.
If those don't work, must be antenna problem on remote or drone. Assuming yours on remote are open and aimed correctly at the aircraft. If so, linking a different remote would solve the problem of whether remote or drone being cause.