All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to reward you for being keen to be kind and dutiful to your parents, and we ask Him to reconcile between your parents and make them love each other so that the family will be reunited.
You should know that it is an obligation to be kind and dutiful to both parents according to your ability. As regards residing with them, then you may reside with either one of them, but since you mentioned that your mother's health is not good, and she might find it very hard to do the housework on her own, then it is more appropriate for you to reside with her, but you should keep ties with your father the best you can by visiting him, phoning him and the like. For more benefit on the excellence of being kind and dutiful to the parents, please refer to Fataawa 87019 and 82254.
Of course, all this applies in case divorce takes place, but we hope that this will not happen. Therefore, you should make every effort for reconciling between your parents. The first thing to do is to earnestly supplicate Allaah to reconcile between them and have trust in Him. A person who hopes for the Help of Allaah will never be deceived.
You may also seek the help of some knowledgeable people whom you think will succeed in influencing your parents. Besides, you may use the affectionate factor and clarify to your parents that you need to see them reconciling so that your heart will be comforted.
Allaah Knows best.