I would call the design company first, because it is actually there problem.

No results? I would call a lawyer!

You hired the design company, not the kitchen contractor. Call the design company and let them know whats going on. No reason for you to fight with someone you don’t have a contract with. Hopefully, you haven’t paid in full yet.

NO NO NO!!! Do not pay extra for them to MOVE the appliances in the house.
Installation means moving and installing. They are just lazy.
How would you NEED to pay them if you moved the appliances already in the spot you want them???

When we specify installation, we mean that we physically move them from where they were delivered to where they will be installed. It often happens that the appliances are delivered before other work that needs to be performed before the appliance is installed, isn’t. And, we don’t want the appliances cluttering up the area until that work is completed, so many clients have them delivered into the garage until my electrician or plumber says the appliance is ready to be installed and all other prep work is completed.

Personally, I would be a little insistent with the design company that they move the appliances from the garage to the kitchen. Especially, if there is other work to be completely prior to their installation. I would threaten to contact the Better Business Bureau and the State Contractor’s Licensing Board to complain. Moreover, this is a very poor example of customer service and I gather they aren’t expecting you to be a happy satisfied customer who will act as a referral in the future!