Well when you say budget doesn't matter... sure it does; are you willing to spend 800, 1200, 2400 or 8000?
If you would like to stay with a DX body my suggestion is to get a D90 or the better D7000 or D300s. If you want to go more towards the pro cameras you're looking at a D700 which has a replacement coming and other higher models.
Upgrading to a FX body will require new FX lenses which are pricier and better in most cases.
My suggestion is to get a nice 35mm or 50mm 1.4/1.8 which would be really good for indoor pictures and really reliable for portraits and decide what camera body would suit you better. Also keep in mind your current camera does not have an internal AF motor so these inexpensive prime lens will not auto-focus unless you get the AF version which comes at a higher in price. If you change the body to a D90 ,D700 or a D300s or higher then you don't have to worry about the AF motor and a cheaper prime can be picked up.
It honestly sounds like you're not using the correct settings for the camera since you mentioned the light is not a problem and 99% of photography issues come from not having enough light or not using the correct settings for the ambiance. Can you post a shot or two and I'm sure more TPH users will give you some advice. Also name a price for what you're willing to spend for new gear as there is a lot of choice in photography gear which all relates to $. You can pick up a lens for 140$ or 1400$ both pretty comparable in terms of image quality, but one will give you more options and uses.
