Hi Judy, Check out this hotline thread, in which this same question was asked. http://www.food52.com/hotline/10035-looking-for-good-braised-short-rib-recipes-that-don-t-use-any-alcohol Lots of great ideas were suggested.

Pomegranate juice also makes a good braising liquid for short ribs.

I've never used alcohol! I use chili sauce with vinegar & brown sugar as my base for r short ribs. They are amazing - I think I'll put. short ribs on my shopping list

Actually, you will not be able to remove all of the alochol. A small amount will always remain, no matter how long you boil it.

Yes you can.
First, do you realize that you can boil the wine separately which leaves the taste without any alcohol !
Otherwise, just make sure your braising liquid has some flavor. Low salt chicken stock with some tomato paste. Add in your mirapoix veg and add water to get volume. Remember your liquid will intensify as it cooks down.
Strain and reduce to serve over the meat.

You certainly don't have to use alcohol. The important point is to use an acid, and alcohols (wine, beer) are common and easy sources thereof. That said, tomatoes are an excellent substitute. I usually use both, but the one alone will give you great short ribs.