There's plenty of great diving on Saint Vincent, I dive there for a week or more and am happy. (I've stayed on Young Island 3 times so far.) Which "other islands" did you have in mind? The Grenadines are not
that close or easy to get to, you would not typically make day trips from St. Vincent to go diving. Even the closest island, Bequia, is an hour ferry ride. (To get to the next island south with a dive op, it's at least that far again.) I've dove Bequia, but I went and stayed there to do it. It can be nice too but I don't think it's better diving than St. Vincent. (IMO the neatest thing about Bequia is the island itself.) I'd recommend going to Bequia if you wanted to add a stay on another island of at least a few days to your trip, but I wouldn't try to dive even Bequia from St. Vincent!
Maybe you could get up early, haul your gear to the Young Island ferry, catch a cab from the other side to the ferry dock. Or find a boat locally to take you straight from Young Island to the dock. Take the hour long ferry ride to Bequia, get to a dive op. I'm not sure how getting there would sync up with their boat schedules. Reverse and get home late. Or find someone with a fast boat you can charter to zip you over and back faster on your schedule - not worth it, and the seas between the islands can actually get pretty big. Fly? It's all just not very practical.
I'd say dive every day on St Vincent, you can also get in some afternoon and night dives with DSV, and even do a couple shore dives from Young Island if you want to muck about looking for critters, there's alot to be found. Do the all day trip where they do 2 dives on sites further north and stop at the Falls of Baliene. (There's some very nice sites further north which aren't dove much.) Spend the rest of your the time enjoying Young Island, you already paid for it.
It is a lovely place to chill.