Yes. I don't see the relevance.
As freakbro says try reading the next line of the post.
Almost all diplomatic and a lot of intelligence postings abroad tend to be "long term", that means they're usually a family posting in any country that isn't "actively hostile" - so the US sending someone to the UK for a role they're expected to be in for a year+ will normally result in any family (spouse, children etc) having the option to go with them, even postings from the US to say Russia will often be "family" ones*.
Now imagine for a second you're in say Russia with your wife or daughter and they don't have the same protection you do under the conventions, and a police officer decides to stop them for a made up offence and they refuse to pay the "fine" - that puts your family at risk but you (and your government) can't do much, now if that stop was directed by the KGB (back in the day, or whatever they are now), it means that your family are now under the control of a foreign government and they could use that very easily to try and get you to hand over information they want, or at least force your government to replace you because you are now compromised (you can't be trusted not to put family over country).
Hence diplomatic staff usually have immunity for their family, there is also an element of the fact that many diplomatic staff may be married to a spouse who is not technically a diplomat but expected to play host at events and offer support, and even official vehicles have a level of immunity because otherwise having the local police harass the drivers of the vehicles is a great way to interfere with the work of the consulate without technically touching the status of the diplomat themselves.
It's all about understanding how and why diplomats have the immunities they do, how in the past shortfalls in it have led to extensions to cover things like the family or official transport.
Fortunately it's relatively rare for a proper member of the diplomatic staff (or their family) to commit a serious crime, as one of the things most countries look for in their diplomatic staff is good behaviour in both the staffer and their family as the last thing they want is an incident in a friendly country, let alone in one that their relationships are less than great.
It's incredibly rare for it to be actively abused with the intent to commit major crimes.
Having said all this, I'm sure I heard that the woman in this case was not covered by diplomatic immunity and neither was her husband, but rather the common case of US military/intelligence personal who commit crimes in a foreign country getting rapidly shipped out and the US playing their "we don't extradite our employees to anyone even for obvious crimes, or even to countries whose law enforcement is respectable and we have an agreement with that allows us to call for extradition of people for very minor offences".
*Most governments recognise that unless you're in a combat zone/high risk area people tend to cope better with family so they're less likely to request a return to the home country which is costly both in money and loss of experience in post (especially true in countries where the culture may be very different or high stress but low physical risk such as say Russia).
