If you're going to stick with your current camera (nothing wrong with that), then you'll likely be better served by having a good quality zoom lens.
While the 50mm f1.8 is a great lens and cheap, and it's also good for portraits of single people or couples, it's not ideal for a group photo because as you discovered you can't get wide enough.
Looking at your zoom lens options, there are a few to choose from:
Canon EFS 17-55mm f2.8 IS USM - a great lens, plenty around secondhand between £250-400
Sigma 17-50mm f2.8 EX OS HSM - similar focal length, perhaps a bit cheaper
Tamron 17-50mm f2.8 - this comes in two versions, one with VC (image stabilisation) and one without, which is cheaper.
Shop around and check out MPB, WEX and Ebay and you could have a good usable lens for less than £300.
One of these lenses will give you a great versatile lens for use in any situation. The f2.8 aperture will be good for low light indoors and to give shallow depth of field when you want it. The image quality from any of those 3 will be much better than the standard Canon 18-55mm kit lens as the glass is better and will give sharper results.
Get one of these and practice, then later on once it's starting to pay for itself, upgrade the camera.
The problem with indoor family shoots is space and light. On a camera like the 550D, it's a bit older, so if the room is dark and you crank up the ISO to 1600, you'll start seeing noise. To eliminate this, add a flash to your kit and learn how to use it, but make sure you also buy a light stand and a diffuser such as an umbrella to give you a nice soft light, and a cheap remote flash trigger like the Yongnuo 522C.
If you can't afford to spend £300 on a new lens, spend £100 on a flash, stand, brolly and trigger and you can get nice results even with using the kit lens.