Wouldn't you need two pins? One on the intersection and the other the location you want to go?
You can use google direction api and set up two waypoints on the each path of the intersection , simply call the api twice with the waypoints included on each call like the following
Api call 1: Send with waypoint 1 as parameter so route includes it (forces it to go that way)
Api call 2: Send with waypoint 2 as parameter so route includes it (forces it to go the other way)
Is that what would need done? 2 waypoints? I'm not a developer (programming), I can design a website but when it comes to JavaScript I know very little.
I guess what I wanted to do was to have it take the leg-work out of trying to find the next nearest-intersection if at all possible, since this would be used in an emergency-services based side. And not everyone is computer-savy.
I know that from the google maps (ui not the api), it is possible to get an intersection of two streets by joining them with an & like in "12th Street & Adeline Street" which will show you that intersection.
If that query works using the maps api (probably the geocode or places api), you can get the lat and long and place them in a get directions api call along with the waypoints i mention to the tune of something like
"direction from (12th Street & Adeline Street) to Bayside Patient Dispensary
via waypoint 1 (adeline street which should return a route going straight up) " and the other route being
"direction from (12th Street & Adeline Street) to Bayside Patient Dispensary
via waypoint 2 (12 streetstreet which should return a route going the long way but passing through magnolia street) "