When we filed for extension I paid $4K thinking we would owe the IRS. Our return says we're getting about $2K back. Will they send me the $4K back I already paid?

Did you enter the payments from the extension on your tax return?  If so the $4K was added to the total paid the $2K is all you get back....  

If you used the TurboTax Easy Extension to electronically file the extension request, Form 4868, and make the tax payment with the request, the payment should already entered on your tax return. Provided you used the same user ID for the 2018 online tax return as was used to use Easy Extension. You can check to see if the amount is on your tax return by clicking on Tax Tools on the left side of the screen. Then click on Tools. Click on View Tax Summary. Then click on Preview my 1040.

The federal extension payment will be shown on Form 1040 Line 17 and on Schedule 5 Line 71

To enter, change or delete a payment made with an extension request (Federal, State, Local) -

• Click on Federal Taxes (Personal using Home and Business)
• Click on Deductions and Credits
• Click on I'll choose what I work on (if shown)
• Scroll down to Estimates and Other Taxes Paid
• On Other Income Taxes, click on the start or update button

On the next screen select the type of extension payment made and click on the start or update button

Or enter federal extension payment in the Search box located in the upper right of the program screen. Click on Jump to federal extension payment