1) "A lot of women have painful allergic reactions to the copper ones" -- No. Copper allergies are rare and occur in less than 1% of the population, according to the FDA. If you suspect you have a copper allergy or are sensitive, you can do a simple patch-test on your arm before considering a copper IUD to check for copper reaction.
2) [IUDs] "have a bad history of getting lodged in the wrong places and having to be surgically removed" -- Also wrong. The most common occurrence of perforation is during insertion, and even then perforations during insertion happen in less than 0.001% of cases. I would not consider this a "bad history" or common occurrence.
SOURCE: http://en.wikipedia.org/wiki/IUD_with_copper & I have a hormonal IUD currently and have had copper before.
Your information about IUDs is over 50 years old, and is based on the copper "coil" IUD which hasn't been in use for decades. Current IUDs (both hormonal and copper) are extremely safe, effective, and perhaps the most error-proof and reliable form of birth control out there. The largest risk with an IUD is rejection, where your device falls out -- the solution is simple, it's just reinserted. The largest barrier to getting IUDs is the belief in the US that you need to have had children first, to have a cervix wide enough to tolerate insertion. This is also untrue. You can have an IUD at any time in your life, insertion is just much more painful if you haven't had children.
Additionally, you don't need to scan a woman's womb before having sex to confirm she has an IUD. You can usually feel the strings from the IUD (there for easy removal) at the top of the cervix, with your fingertips. And if you're a man worth half his salt, you'll have had the opportunity to... check that out before having sex with her ;)