That said, if you are committed to your idea, do what you have to in order to get it off the ground, but don't give away the keys to someone you don't trust. If it were up to me, I would not trust Network Solutions to build my product.
You can build trust by giving those involved a stake in the idea. Make your gains into their gains, and your losses into their losses. The relationship between you and your team should be less "boss/employee" and more "founder/co-founder".
You can't do this with NS. What incentive do they have to build the best product you can build? What stake, beyond your tiny slice of their revenue, do they have? What guarantees do you have that NS will not hold your product hostage in return for lackluster support? These are the questions you should be asking.
I'm curious; are you a developer? I see this type of situation all the time in my field of work, and it's usually large companies taking advantage of entrepreneurs who aren't tech-savvy.