I agree with everyone else, that she is more comfortable around you, maybe because you handle her much more or are around her much more. It is really nice to have a horse like that with you, but it can become a problem if they are very uncomfortable with other people.
It's important to maintain a happy medium, which is having a horse that is equally comfortable around their owner/s, other people and other horses. Having a horse that drifts to close or too far from either of the above can become an issue. You want a horse that won't freak out when it is removed from a certain person or horse, as well as accept handling from different people.
What I suggest you do is start introducing her to several different people (not just family and friends), and get other people to handle her as much as possible, not just only you. It's important to address problems as soon as possible, before they get bigger and stronger, thus more difficult to handle.
One thing you can try is to give the leadrope to another person and let them groom and handle her while you stand a few metres away, close enough so that she can see you, but far enough so that she knows that she is being handled by someone else and not you. This will help keep her calm enough to not spend all the time with the other person stressing about where you may be. As she gets better at this, remove yourself completely from her sight until she is relaxed at being alone with another person.