My best friend lived on Kotenburg Avenue growing up, and I lived on Willow Glen Way (next to Nevada) and understand your concern living near a main street such as Minnesota. Kotenburg had more foot traffic than my street did, but the vibe on both streets was and is the same, very friendly, family oriented and SAFE. I would feel comfortable sending my kids with a nanny downtown WG and not have any concern with the kids/people you refer to as "shady." People have been hanging out at Quik Stop forever and I don't think that is going be changing any time soon. The family that owns the store are amazingly friendly and actually there is usually a police presence around (I'm not sure if it's Starbucks or just the parking lot they hang out in.) Let me put it to you this way, I'm 30 and over the years I've walked, bicycled, driven by this corner daily and have never seen anything ever go down there, from a fight to a drug deal. Minnesota is safe at night besides a speeding car here and there. I think it's safe enough to allow the kids/nanny out front to play, I would just tell them to watch for cars as you would on any other street. Traffic is definitely slower on Nevada but it's also a smaller street and not a cut through street like Willow Glen Way and Kotenburg (but much more Blewett and Settle.)
Pick up a Willow Glen Times downtown WG to check out recent crimes in the blotter, ALSO if you already haven't , check a megan's law website to make sure there are no child molesters living near you...Good luck with your search!