At home, it's quite often low light (curtains shut, low wattage light bulbs). I usually shoot at f/4 (aperture priority) because I find with moving children f/4 gives me a better chance of catching them in focus. The camera is set to auto ISO, and I have the shutter speed limited to 1/60 deep in the settings (any slower can give blurry pics). I think the camera can override this setting if it has to though.
I had a Canon 50mm f/1.4 USM years ago but a hell of a lot of shots were out of focus because I kept trying to use the lens at f/1.4. The odd one that I did nail did turn out very good though.
I know that 'dragging the shutter' at lower light with the flash can give excellent results, but I don't like to think too much about camera settings when taking family photos because it's more about capturing a moment that could be lost If I had to think about adjusting settings. I have a lot of respect for wedding photographers.
EDIT:
I always shoot in RAW.
I know all about the moving child photography dance, it can be quite a challenge... It would be worth finding out what ISO the camera is choosing for you, as this will define when things get gnarly (everyone is different as to how much noise is acceptable). Basically, you need to find out when things work, and when they don't for you. e.g, if the ISO is 6400 then it's fine, but any higher and it's a problem, then you'll know how many stops you need to gain vs what you currently do to give an acceptable image quality with your current kit. Let's assume that you need to gain two stops to get the image quality you want, then this could happen by changing other aspects of how you shoot, rather than the camera. For example, if turning the lights up a bit gains 1 stop, and opening the aperture to f/2.8 gains the second, then you've managed to get where you want to be without new equipment...
I'd also try shooting JPG rather than RAW for a bit, or I think you can enable JPEG + RAW if you are unsure, to see whether the built-in JPEG engine does a great job of removing noise (you may find it's better than what you do with the RAW files).
On your camera settings, I find that cameras like this hunt around trying to focus in low light, and either get it wrong, or take 1/4 second to get it right, and this lag makes taking low light photos of moving subjects much harder. The way I resolve this is to change the camera shutter behaviour from it's default (1/2 press to focus + exposure lock) to just exposure lock. I then make the '*' button on the back act as the autofocus control. I also set the camera to 'servo' focus. The overall effect is that you depress and hold the '*' button, and the camera keeps focussing, adjusting as the subject moves. Then, pressing the shutter takes a photo, never any delay or lag. You can also grab focus, release the '*' button, and recompose to take a photo with an off-centre subject. I'd certainly try this sort of setup as it works really well for me. The main downside is that I can't quickly explain it to someone else if you want to be able to hand the camera across and have someone else take a photo.
You're choice of f/4 is surprising - i'd try f/2.8 to see if the depth of field is enough, and if so, this might resolve your noise issues by gaining a stop.
You mention problems with the 50/1.4 wide open - absolutely, it's not easy to shoot with, as on a cropped camera body the framing is tight, and the depth of field very narrow. A quick check on a DOF calculator says with a 2m focus distance, you'd have 8cm depth of field, which is just about an eye to an ear, or something like that. If you were to try a 35/2 IS at 2m, you'd get 24cm in focus, which makes a huge difference. Also, you'd have 2 stops more light compared to your f/4, so this again might be worth considering.
So, to summarise, try JPEG in camera, try shooting at f/2.8, try changing camera settings to improve your hit rate in low light, if all else fails, consider a faster lens, and then if none of the above help, consider whether a new camera might help.
