I reckon taking indoor photos of kids parties has stumped me more than any other photography.
Easiest thing is a wide angle point and shoot and use flash. The greater dof keeps everyone in focus and the flash lights it up. So if you got one use it as a back up.
When using the DSLR and a lens with a big aperture like the 50 1.8 you don`t need a flash for lack of light, but due to the narrow depth of field the only thing in focus is what you are focusing on. This may not be your subject, you need to carefully pick your focus spots. Then the interior light can throw out your pictures and colour tones, pays to shoot in raw for that. But my 5 year old Sony handles indoor awb better and more natural than my new Canon does, if I just compare jpgs.
Its great to isolate a kid or a cake with using the DSLR and your kit lens will be fine for that.
A good idea is to have a few practice shots prior to the party to get an idea how the colours, lighting etc comes out, increase your iso, or use your build in flash. Play around with spot focusing a subject. Instead of kids sitting around the table with the birthday cake, do it at dinner time with similar lighting.
My Sony A100 auto focus is slow and was the main reason I wanted something faster, but indoor shots isn`t the problem it was outdoor with plenty of light and action shots.
Basically what solved most of the issues I had was an external flash, bounce the flash of the ceiling and light up the whole room. Solves the problem of indoor light, low shutter speed, focusing issue
( flash has auto focus assist ). Its also very handy when taking outdoor shots of kids, think wedding photographers, as it lights up their faces.
So what I am rambling about is that I cannot give you advice on lenses, I was disappointed with the upgrade path and high cost in lenses from Sony and switched to Canon, but would suggest and external flash and have a good practice before the event.
Canon Powershot S95, Canon 6D,7D, Canon 40 2.8 STM, Tamron 24-70 2.8 VC, Canon 17-40 L, Canon 15-85, Canon 85 1.8, Sigma 30 1.4, 50mm 1.8, Canon 100 2.8L Macro, Canon 70-300L +Kenko 1.4 Pro 300DGX, Canon 430EX II and RS 4 Classic