C.,
I also have a three-year-old and a four-month-old. I also have a business that I run out of my home. In addition, I teach a few classes at a local college. My four-month-old is similar. Without knowing your child or you and your husband, I am not comfortable making an assumption on why she has this behavior, but I can give you an educated guess.
If your daughter is with you or your husband most of the time then she has become accustomed to the way you and your husband talk to her, hold her, comfort her, etc. If she is not with other people, like a babysitter or grandparent, on a routine basis, then other people's touch feels foreign to her. Also, I don't know how you and your husband parent her, but if she is held often and walked around then she would not be content to be held by someone who sits down or holds her in a position that she does not like.
Socializing a baby is like socializing an animal; however, it is not healthy or safe for babies to feel comfortable with strangers. We don't want them to hold out their arms to everyone when they are able to say who they want to go to. Wanting you for safety and security is a good thing (to a point)I would allow more trusted people to hold her when you are not in the room or if you must leave her in their care. I would not, however, let her cry while she is in someone else's arms and she knows you are there. I think that is cruel. You are her parent and the only way for her to communicate to you and your husband that she needs you or feels vulnerable is to cry.
If you are breastfeeding that may play a role also. I do breastfeed and my four-month-old will be content in someone's arms until I walk in the room and she smells me.
Good luck.