Maybe I'm misunderstanding but it sounds like you hired a company who offers web design/development as a bolt-on service to IT work. If I've got that right, this was your only serious mistake.
Web design is not an IT skill. If you're serious about your brand's online presence, you need to hire someone who makes web design their core business.
There are applications Wordpress is not appropriate for, but I seriously doubt yours is one of them. Rathji's right that you need a good developer to work with it, and that if your developer starts talking about what theme to use, you have the wrong designer (unless your total budget for this is $500 or something, in which case you can ignore my entire post). The theme should be "killer_carlson's custom-built theme", and the project overall should be treated as any custom web design and development project would be.
(start rant)
The thing that kills me about so many freelancers and small web shops is that they sell a service instead of a product. They charge hourly, engage in lengthy back-and-forth with the customer, they change button colors, they make the logo bigger, they add "pop" when a customer asks, and usually don't know what user experience means. All of this is wrong. You'll know you've found a good web shop when they treat it like a product.
They should be asking
you the questions. You should leave your first objectives/requirements meeting with them surprised at how much stuff
you never even thought of. It's their responsibility to extract all the information they need to deliver a product that delights their customer.
When you ask for a pile of changes, they should fight you on it because they're professional web designers and they've spent more time thinking about that button's color than you have. They shouldn't let you get away with giving it a once-over on an iPad - when they deliver the finished product to you it should be in person (if possible) and they should be taking you through every detail. Every product they deliver is an extension of
their brand, and they should be excited to deliver it to you and to add it to their portfolio.
(end rant)
ETA: Rathji doesn't really hate Wordpress