Is there a compiled widget out there that would allow the user to enter 2 street names and the widget would zoom into the intersection of these streets?
If you have a geocode service that uses street centerlines or point intersections (or even both in a composite geocoder), then you can use the Locate widget. Intersections can be typed in using the following syntax: Main St and First St - of course, however you have the streen name syntax set will change that example.
Here is a link for address candidates using our geocode service. You will see I simply typed in "n green river and morgan" and received two results (makes sense, the roads are separated lanes so two centerlines).
Depending on how you set up the geocode service (via the address locator), will determine how you can search intersections.
If you create the address locator using street centerlines, then all intersecting nodes can be searched using the "First St and Second St" syntax.
If you create an address locator using a point feature class, you need to ensure you have a field with the intersection name. Here is a link for creating that: