I'm amzed no-one's asked this yet, but who made that frame? Normally I wouldn't be surprised if you didn't tell anyone, but this is such a major problem that the world deserves to know.

Anyway, whatever you do don't ride it! Even if you can get the cups to stay in (with blue Loctite BTW), and even if you can get the chainline right (not bloody likely), you still run a major risk of knackering your BB, which I doubt the frame builder will warranty. BBs are designed to spin in one direction, and often have two bearings on the drive side. Running it backwards will put undue stress on the single non-drive-side bearing (if that's how your BB is made anyway), and you could end up without a BB AND a frame. Len is right, get them to send the new frame to your LBS, then send them the broken one. Make sure you get proof in writing that they will send it and pay all the shipping and labour costs.