Thanks ladies.
I did not install any of these tires. It was my LBS. I know he said it kept puncturing in the same spot again and again. On either side of the valve. Strange thing is, it's been BOTH of the rims. But only AFTER we replaced the tires with Kevlar ones. (Again, oh the irony. Alanis Morrissette style irony, but still.) "Your bike tire pops, when you've already paid."
Took it in to the LBS. The rims I picked are basic with sealed bearing hubs and nice spokes. But I guess Weinmann DP18s aren't exactly well-made. I was told to leave the sticker on the rims by some friends because it hides the ugly welds underneath.
You get what you pay for. *sadLOL*
We'll see if the LBS can get things straight before the St.Pat's Day Parade here! Our cycle-project group were planning on riding in a big group in the parade. I put some more green accents on the bike in anticipation.
Hopefully, it will be ready to go by then.
If not, I can ride another.
Thank you for the advice. So, so much. 
Anyone else have some thoughts?
"Things look different from the seat of a bike carrying a sleeping bag with a cold beer tucked inside." ~Jim Malusa
2009 Trek 520-Brooks B-17 Special in Antique Brown
2010 Surly Long Haul Trucker-Brooks B-17 Standard in Black
1983 Fuji Espree Single Speed-Brooks B17 British Racing Green