Calendar with multiple content types on multiple field types
You're not going to get Views to add the 2nd content type (and only the 2nd content type) in this way, at least not through the Views UI. You could do this by programmatically altering the view's query or something like that, but it would be no fun.

I would recycle the "date" field from content type a into content type b and set the default value = now; that way when a new node is created it will have that value by default.