When you say "too tight", what exactly is meant by that? You'll have to excuse me not knowing the terminology. I am still a dummie when it comes to cameras.
It means that the subject may be too large at 85mm. An extreme example is to put your 55-250mm lens and zoom all the way out to 250mm. Now try to take a photo of a person standing 5 feet away. The subject fills way too much of the frame. When you are working with a prime lens (one that doesn't zoom) you control how much of the picture frame your subject takes up by moving closer or farther away from your subject with your feet (thus the term zoom with your feet). Indoors however you're often limited in how far away you can get from your subject. So, while an 85mm is a great length for infants and a great length for head/shoulder shots of adults. Once your kids get to toddler stage it can be tough to get the full body in the photo frame indoors.
To answer your other question, Sigma is the name of another lens manufacturer. Sigma, Tamron, Tokina all make lenses with various camera mounts (nikon, pentax, sony, canon etc.) So you can buy a sigma lens that has a canon mount on it - that lens will work on a canon camera.
Wider than 85mm, the next step down is typically a 50mm lens. There are several options - the Sigma 50mm 1.4 is probably the best on the market in your price range but I think at your stage (infant) the 85mm is a MUCH better lens.
Some shots with the 85mm 1.8: