Can a party change her mind and disagree with mediation agreement the next day?

You need to talk with your attorney about this. Your attorney will know if this was binding mediation and will know if you have recourse to change your mind.

Ask your attorney to explain Superior Court Civil Rule 2A, regarding the admissibility of agreements between the parties. If the court views your verbal agreement (was it recorded?) as having been "signed", then it will allow the agreement's terms to be admitted into evidence. In most cases, the court will enforce the agreements of competent adults, especially when they are represented by counsel.