How do I start the divorce process and what are my options since I'm on a fixed income?

You begin the process by employing a competent and experienced family law attorney to represent you. The effort necessary to do that now will save money, time, and heartache in the future. As regards your custody issues, the Court must comply with the request of the older child, if the the Court finds that choice is in the best interests of the child. The Court must listen to the wishes of the 12 year old, but the judge is not bound by that choice. He must likewise find that the choice is in the best interests of the child. These decisions ultimately affect the determination of the child support obligation of the parties.

Let me stress that having a lawyer matters, so step one is see one. The adultery matters far less than you think. The best interests of the children and the finances will dictate most of the result.