I'm going to have one more ps3 console. Is there any way I can connect my old HDD to the new PS3 and play different games on both of them at the same time ?
No, a hard drive can only be used by one machine at a time.
The PS3 also does not support playing games over a networked storage system so that's not an alternative.
However you maybe able to copy the game onto the external Hdd to play on one console, while playing another game on the other console via the internal HDD?
To go further, this isn't specific to PS3 Hardware, but to HDD hardware. There's only one bus. Only one set of read/write heads, therefore it's impossible for a regular disc to be commanded by more than one computer. Moreover I assume there would be a firmware protection to prevent this.
Side Note: As Kevin van der Velden sated, "PS3 also does not support playing games over a networked storage". But in the case of a NAS, if PS3 had the ability to play game over network, this would work because the HDD is controlled by an abstraction layer that can parallelize disk access and file lookup
So, for your problem, one solution would be (I'm no PS3 expert, but I do same kind of things on my Wii) would be to fully load the game in your PS3's RAM. If a such thing is possible, then you can launch one game with your drive, unplug it, as there would be no reason to access the HDD, and plug it to your new PS3, and load an other game