Think about how your two 'resident' cats feel. All of a sudden, this new thing (that it's a cat is immaterial to them) has come into their home space, is taking your attention, and is walking up to them without a care in the world and making them feel like strangers in their own home.
Cats are territorial animals and resent another trying to invade their territory. The weeing on your bed is classic stress - trying to mark territory and show unhappiness at the same time. Your bed is the one thing in the world that smells to them most strongly of you - they're quite literally putting their scent on top of yours, saying 'hey, we're part of this family together'.
What to do? Short answer: leave them to it - some fur will inevitably fly, but they'll soon settle down into a new pecking order and will accept the newcomer - they may become the best of friends with the newbie, or they may grudgingly tolerate her - mostly depends on their personalities.
Otherwise, you could do it the more hands-on way - groom the newbie with a brush, then groom your own cats with the same brush - maybe rub the newbie with a towel/glove, then do it to your residents and vice versa - this transfers the scent and makes all parties seem less strange to each other. Get out a favourite cat toy (theirs, not yours
) and play with it while they're all there. Finally, take a look on [broken link removed] and
www.fabcats.org for more info on introducing new cats into the house.