The short, and often sad, answer to this question is yes. If you cannot prove that a domestic violence claim alleged against you is false, then you do risk a change in custody. Divorce is a stressful situation on all by itself. Add children and custody battles to the mix, and things can get messy very quickly.
Unfortunately, there are some parents who are so against co-parenting with a soon to be ex-spouse that they will stop at almost nothing to prevent that person from any kind of custodial award, including filing false domestic violence claims. For this reason, it is best that parents who are navigating an emotional divorce and custody battle speak to each other as little as possible. Think about when you were married and you would get into a heated argument. Maybe you raised your voice at times, or even touched your partner on the arm to get their attention. Now that custody of the children is at stake, those actions could very well be used against you.
Once a domestic violence allegation has been made, it is then up to a judge to decide who is telling the truth. Most importantly, he or she must decide what is in the best interest of the child. An emergency order of protection may be issued immediately, thereby banning the accused from any contact with the child. Once this is issued, any mere suspicion of a violation of that order could cause you to lose custody permanently. Though this is a possibility, it does not always happen this way. In fact, sometimes a court can even decide to allow an abuser to continue parenting time. Every situation is unique, and each must be taken into account as a complete, big picture. If it is found that continued time with that parent is still part of what is in the best interest of the child, then that is how a judge will rule. Sometimes best interest factors, when looked at collectively, can outweigh a single occurrence of violence between two parents.
Regardless of the reason, if you have been falsely accused of domestic violence and custody of your child is at stake, it is highly advised that you immediately consult with an attorney. He or she can help you gather evidence to prove your innocence, and protect the relationship with your child.