In family court, can I have my attorney go to the custody hearing without me?

Your attorney cannot appear for you at a hearing. You will likely have to testify, and be cross-examined (and perhaps questioned directly by the court) and you need to be there for such to occur. If you do not live in the local area, your attorney can request that you be allowed to appear by telephone if traveling is a financial hardship. However, you need to be aware that Judges rely on being able to visually "size up" a witness/party to decide who is telling the truth and what decision is in the best interests of the child/children involved. That is hard to do when you are on the phone, and impossible to do if you are not present. If you want the best chance of "winning" you need to be there in person.