One other idea is to knock down the amount of light coming in (as opposed to adding interior lights).
If you have the money, get a roll of Lee Scrim; it’s pricey but very reusable. Just tape it up on the OUTSIDE of the windows that are problematic in the shot. Lee Scrim cuts the amount of light coming in by about 75% (or two stops) and the camera (generally speaking) doesn’t see it. Great stuff. If you can’t reach the outside of the window, you can tape it to the inside but this takes longer because neatness counts. (Use paper tape and be gentle.)
Don’t worry about putting the Lee Scrim over the windows out of the frame: those windows will in essence “boost” up the interior lighting.
Lee Scrim (or Rosco Scrim) comes in a silver/black version that is silver on one side to create a reflector should you need one. You can also get it in a black/black version. You want the black side to face the camera lens.
Look for Lee Scrim (or Rosco Scrim) at a film/video expendables store or a local theatrical lighting store (they will probably need to order it for you).
If you’re on a budget, you can try getting window screen at your local hardware store. You’ll need to experiment to find the right density for your needs.
You may find that a combination of adding lights and knocking down the windows will give you some of the best results on a budget. But I agree that to do it properly you will need more than one light.