While it is possible to use a mailmerge with two or more source files, doing so isn't something that seems appropriate to your situation. I'd suggest employing a user-form with listboxes that you can populate from each of the source workbooks. Once the client and hospital are selected, a command button could be used to populate bookmarks in the document. For some code to populate userform listboxes from an Excel data source, see:
http://www.gmayor.com/Userform_ComboBox.html