Blurry motion with iPhone 4s - scenario explained

Question

I am indoors for these photos - however - I am by 4 very large picture windows - the lighting is GREAT.
I have a 9 month old and we are CONSTANTLY getting CRAP pictures! If she moves her arm or anything - we get the blurry arm... Even moving her mouth will make the mouth blurry.
I take with my P&S Nikon (that is pretty old and crap) I get NO issues with the camera. My old Droid 1 took great pictures in this light - so I really know it isn't the lighting.
The camera is great on the 4s - don't get me wrong - but I am sick of so many pictures that shouldn't be crappy being crappy.
I have the flash set to auto - so it'll use it if it needs it... but it never does for these pics.
Any recommendations? Would love some help on this - is there any way to enable more manual control am I missing something? HDR is not on - as I have yet to really see why that take any better pictures... at least when I am in my living room.
Thanks for any recommendations any of you might have. I love the phone - I was REALLY excited about the camera.
Oh - and I have NO PROBLEMS WHATSOEVER  when I'm taking video in the exact same light.
I have a white iphone 4s.

Answer 1

Good Afternoon All,
Yesterday I went to the Apple store/genius bar. First of all I had the clear protectant film on the front and back of my phone under a two layer incipio case. The rep that helped me stated there should be no film on the back of the phone as it causes reflection from the flash causing haze with pics ESP at night/darker environments. I admit I was skeptical and he also said that my case while nice did not have a large enough opening for the camera lens/flash even though it was made for iPhone 4 the changes made to the new camera calls for a sizable difference in the opening to allow for the flash to work properly.
I purchased my case at Verizon and they told me no such thing, so I was a bit skeptical but I picked a case with a larger opening approx a 1/2 centimeter larger than my current one and removed the film from the back of my phone then I asked the rep if he would go into the back area of the store, turn the lights off and take a few pics to be sure that was the problem and he did!  Viola! Problem solved. I'm really surprised that was it but last night I took a bunch of pics in low level light and they turned out great, no further issues. The brand of the new case was "uncommon" most of the cases for 4s in the apple store had a much larger opening and the inner part of the opening was also blackened. There were a few other brands too "speck" was one but if you are buying from a website just make sure you get one with an opening of about 1/2" H x 3/4" W to. Accommodate changes made to the camera.
Hope this helps others.  Have a great day :0)
-Sara