Thank you all for you suggestions! I am going to try the X-pen thing. It sounds logical that my dogs need to be introduced to the new one slowly. This sounds like a good way to do it.
When the new pup came in he immediately wanted to play and did pounce on the Maltese. That was probably what set the Maltese off and the Yorkie just followed his lead.
Thanks again YTers. You always come through!!