A Chinese Elm will do well indoors under the right conditions, and even better outdoors. From spring to early winter, keep it outdoors as much as possible. When it's indoors, give it as much direct sun as possible. Try to get it cool enough in winter to stop growing and drop some or all of its leaves. Outdoors, avoid winter temperatures below 20 degrees.
During periods of growth, trim all new shoots to 3 leaves. This will give fullness and small leaf size. If not done, the leaves will get progressively bigger, and the inner leaves will yellow & fall off making the tree look sparse.