Hi Karen - yes I know what you're asking and yes, it's quite unsusual - but here is how I discovered it was an iframe - I clicked the 'view source' button in FF and I saw - view this frame only - and it shows http://0000qfx.previewcoxhosting.com/ as the url - there is no dlsengineering website so to speak.
Further to that - I've not seen this before and don't understand why it's been done like this unless it's some part of automation on their side when a site is setup but even that seems strange because putting this whole thing in an iframe may have been done manually.. this is my guess only.
I think they use the previewcoxhosting url with a wildcard setting in the dns records (like we do for our development urls), but in an akward way.. we have an xdweb.com domain for testing and development - and no matter what url you put in, the xdweb url will resolve, but if there is no setting in IIS, it resolves to a default website. But in this instance - on your site, it seems like there is a manual setting when you developed the website, but not carried through to point the url correctly.
I think you need to ask them to see that the http://0000qfx.previewcoxhosting.com/ url in IIS is replaced with yours rather than wrapping in an iframe - that is what I would be asking them.
It's as simple and as messy as that.. and definitely fixable. I wonder if they have setup two accounts for you or something inadvertently... who know..
Nina