I spend quite a lot of time in Dubai and would say that most people are relaxed and tolerant. That said, you can only push that tolerance so far and I would never have sex in public. You need to understand that having sex outside of marriage is against their laws and, to do it in your own home privately is one thing, but to do it in a taxi is making it impossible for them to ignore....
Facing some jail time for having sex in the back of a taxi is not disproportionate and I will add that the man will normally face the same penalty. In light of the woman's nationality, it's likely she would simply be deported if the foreign office decided to weigh in.
You would be an idiot to be snogging in the back of a Dubai taxi, forget anything else. As I said, locals are tolerant but you should also be tolerant to their laws and culture. If you are sensible, keep displays of affection reasonable and respectful and make sure you only have sex in your own home (hardly onerous conditions...) you won't have any problems in Dubai.