AFAIK po, ang may diplomatic immunity ay ang DRIVER at hindi ang sasakyan. The embassies use local drivers also and if they violate laws and such, I believe they are not immune.
As for the diplomats themselves, yes, I believe they cannot go to jail -- just as our diplomats in other countries can not. Pero if they have a violation and/or commit a crime, puwede silang i-boot out of the country by being declared persona non-grata.
Unfortunately, extremely few of our enforcers know this -- let alone bother going through the process of booting out scalawag diplomats. Unless malakas din ang makabangga nila.