Tea-
My partner is somewhat shorter than I am in heels...about 2". So I can appreciate the difficulties that this may lead to, especially in smooth and modern!
There are a huge number of reasons why you may be off balance in your turns that are not related to your height difference. Vince's last comment especially seems to indicate that he may be "stirring the pot" or in other words, forcing you to turn. Also watch out for shorter men as they sometimes have a tendency to bring the arm down too quickly (before you have completed your rotation) which not only compromises your balance but also puts your shoulder in an uncomfortable position.
You can of course always turn under your arm. Most women think that they need more roomto turn than they really do. If your own hand is higher than the top of your head then you can obviously turn under it just fine. Even 1/4 of an inch is enough. Actually, keeping the arms as low as is practical will help with your connection and your ability to move quickly into the next pattern.
Finally...I might ask what discipline of dance you take? I have found that some American style coaches teach Underarm turns quite differently than International style pros. My partner and I have found that the Int. style works much better and is more comfortable for both of us.
M
