I think:
1. You made your bed, now you're complaining you're being forced to lie in it.
2. You should have never started the job without a written contract and an electrical plan.
3. You need a lawyer, not an on-line forum.
4. You need to consider this Lesson #1 in Contracting in the School of Hard Knocks.
5. Is the cost of not putting in that 3-way worth the headache, hassle, trouble and monetary expense, not to mention the damage to your reputation?