I just did a search for the Pico2000 card and found a photo which suggests it's the very same card that I use - previously I'd considered mine to be somewhat unbranded and hence didn't know what it was.
However, it is recognised at a card type 77 (Grandtec) however my working modprobe options are simply options bttv card=77 tuner=-1 radio=0 however as your extra options are zero anyway it might be that they are the default. Give it a try anyway though just in case.
However (again!), I've currently only got one camera connected to perhaps the problem is when there're two. Or do you still have problems with just one camera connected (to the second port or whatever)?
[Edit: Just noticed that your config line is exactly as per the Wiki so perhaps the options are fine as they are... Could perhaps be a dodgy card then? Is it the same port each time that gives problems, or is it just when you've got two cameras connected?]