I think you should not enter the Mandir and stay in the car. Because as an Amritdhari you are distinctive and even though you are planning on sitting at the back you will still be seen by others and they will assume that you are worshipping there. I know how animated Sikhs get when they see other Sikhs being present at places where non-Sikh worship is taking place. Say if a Mona and Keshdhari Sikhs who also go to the Mandir see you there then the next time a Sikh tells them that they should not be doing murti puja at a mandir then they will the fact that they saw you an Amritdhari as some sort of justification of their own manmat.
Yes Sri Guru Nanak Dev ji went to mecca but he went to teach Gurmat. The reason for the Guru going to mecca is the most important part, so why leave it out? Leaving the reason out means you are purposely distorting history for your own views.