Yeah this iFraming business is the main issue - it's to do with your hosting: it's basically a cheap hack to host multiple sites on a shared hosting account (most likely) or a bad domain name registrar using 'web forwarding' or some other such annoying 'feature'.
This sort of thing is by no means an inevitable result of hosting multiple sites on the same webspace.
I have been using 123-REG for both domain registration and hosting for several years. Until recently I used web forwarding, they now also offer a Domain Mapping facility. Neither result in what we're seeing here.