Well, there actually wouldn't be a much larger explosion, that's just not how nukes work.
A nuclear explosion is an incredibly delicate process, and the material just won't go critical because there's another detonation nearby. It's not like dropping a bomb on a dynamite warehouse. There's not a great analogy for what it is like though. Expecting a satellite launch to happen because you blew up a tank of rocket fuel next to it? Not quite there.
Additional contamination from onsite material is a different matter. Most nukes detonate above their target since that maximizes damage, but it also reduces fallout. There would, however, be vaporized material that would be sucked into the air by the vacuum created by the detonation. It's not clear if the presence of radioactive material would make it significantly worse than the general "radioactive dust and molten sand" that would normally be sent into the air.
In general, if you nuke something there's going to be radioactive issues afterwards, and you shouldn't do it. Adding a nuclear facility to the mix is kinda just throwing rocks at the windows on 9/11.