I assume di sya kaya tanggalin nung hinugasan mo yung kotse mo with water. I also assume you tried washing the car with car shampoo. If both assumptions are correct, di rin sya matatanggal ng sabon, but you can definitely try - no harm in trying. :D
As for the watermarks being a week old, the general rule is to take them out as soon as possible (ideal scenario is to wash the car as soon as you get home when it got rained on - but that's not feasible if araw-araw ang ulan, right?). I'm sure kaya yan matanggal even after a month - with the right tools/chemicals. Have you tried using your quick detailer? If that doesn't work, seriously, try out the vinegar solution I mentioned.

it won't eat through your glass coating. Your coating should be able to withstand the pH of the vinegar solution - if not, you chose the wrong coating hehehe. Or if you have the cleaner wax, try that as well.
Also, in case you haven't noticed, medyo hard ang water natin dito sa Pinas, or at least in most areas of this country. Meaning, possible na kung binuhusan mo lang ng tubig yung kotse after it rained to take out the rain water, mag-watermarks pa rin dahil sa minerals na nasa tap water natin. If you can attach a filter to your faucet, it might help lessen the chance of your tap water causing the watermarks later on. I learned that the hard way. I was advised by the guys who coated my car na buhusan ng tap water pag naulanan in case di ko kayang hugasan agad. So a month after getting getting coated (and washing every time it gets rained on), I got home late and didn't have time to wash so binuhusan ko ng tap water to get rid of rain water. Kinabukasan, nag-watermark yung mga nag pool at nag dry na tap water. After that, if it rained and I cannot wash, I leave it as is. Mas di pa nag-watermark yun (compared sa unfiltered tap water).