There's no connection of any kind between the hosting of your business server, the forwarding service, and your home broadband? (Well, obviously, they're all on the Internet, but that's not what I mean.)
How is the forwarding done? If I've read it right, customers ask for
http://www.mybusinessname.com/ and get back a page not from that address, but from
http://www.myrealsiteaddress.com/It might be not your broadband, but some hyperactive security software on your PC spotting some kind of dodgy-looking forwarding? Have you tried using a phone on your home broadband as well as a PC, to see if the same thing happens?
On the premise that URLs are not normally confidential, you could always post the real addresses and let us play? We promise not to buy anything