You will be fine with a kit of only primes. You may need to need to move quickly at times and get good a quick lens changes at events or for kids that are moving quickly, but generally speaking primes are great for the type of photography you describe.
The 85 1.8 lens is great for portraits and general use on a crop body, but at the long end for indoor use (136mm FF equivalent).
I suggest a 35mm (Sigma 1.4 or Canon 35L) or Canon 40mm pancake to use as your normal lens. I love my 50mm 1.4 lens on my full frame 6D, but think you would be happier with a 35 or 40 on T3i.
The Canon 24mm 2.8 IS would be my other recommendation at the wider end. Unfortunately, 24mm isn't that wide on a T2i, but Canons wider primes are either poor (20mm) or specialty lenses, not necessarily useful for general purpose shooting (15mm Fisheye and 17mm TS-E).
At the longer end, the 135L is one of Canons very best lenses. It has awesome sharpness and color rendition. Pictures with this lens just look different/better. Not sure why, but they do. The 135L will be pretty long on your T2i, so if you don't think you will need 200mm equivalent now, you could hold off on this purchase until after you move up to a FF body.