How can I connect a PS3 to two TV/ sound systems in two different rooms?

Audio-wise, you are in luck, since you wish to use two different connectors and the PS3 can be instructed to output audio through several connectors. Simply connect both sound systems to the PS3 at the same time and turn on Audio multi-output and you should be good to go.

Video is another matter, since you only have 1 HDMI connector on the PS3. The only option I see here is to use an HDMI splitter. Be aware that a proper HDMI splitter usually requires additional power to work properly. It should be a box that comes with an additional power supply, like this:

And not a simple cable that splits in two, as these typically do not work (and technically, I'm not entirely sure they can work. I've never seen one with positive user reviews):