Developmentally, your three year old does not have the verbal skills to identify his feelings and explain his feelings. You are probably getting acting out behavior because he misses his daddy. Ask him if he wants to talk to his dad. Dial the telephone number for him and hand the telephone to him to talk. You can let your ex know the first time that you are putting him on the phone, but from then forward just dial the phone and let your son talk. Talking to daddy a few evenings a week may be all it takes to solve the problem.
I would encourage you to try to limit the power struggles with your 3 year old. Kids like choices. "Honey do you want to take your bath before or after supper?" "You need to pick up your toys. Do you want me to help or do you want to do it by yourself." By asking him to do things in that way you are giving him some control over his life. Children have lots of choices to make as they grow up. If you can start now teaching him how to make choices it will really pay off when he is a teenager. Don't ever forget...if he is having a tough time right now the best person to take it out on is you. You love him unconditionally and he knows it. No matter what he ever does you will love him and he knows it. That is not a bad thing. It gives him a space to act out the frustrations that he does not have the verbal skills to communicate yet. He is having a tough time. Just love him through it.
Instead of getting into an argument ask him questions and divert him. "Who loves you as big as the sky?" Mommy does. Daddy does. Grandma and grandpa do. etc. "Who loves you as big as the ocean?" Mommy does, etc. "Who do you love more than all the leaves on the tress?" He loves mommy. He loves daddy, etc. When my children were on my last nerve it always reminded not only them, but ME how much I loved them. Pretty soon this little game will divert him. Then ask him, "What toys do you want to play in the bathtub with tonight?" And he is telling you what toys and getting in the tub. Sometimes my 3 year old will say, "I don't want a bath tonight. Can I take one in the morning?" and I say sure, but we have to get up earlier to take one in the morning so you will have to go to bed a little earlier. You can start at 3 years old negotiating with them. Make it his decision if he wants to go to bed earlier and get up earlier to take a bath in the morning. Start now giving him choices. Life is all about choices and the more you give him choices the more "in control" he will feel in a situation where he has no control--mom and daddy are divorcing. Giving him choices about other areas of his life will help him through it.
There are great child therapists that do play therapy with 3 year olds in every community. Call your local mental health center or child advocacy center and get the names of 3 or 4 of the best children's therapists in your community and schedule an appointment. Your little one may just need someone to talk through what he is feeling.
Good luck to you and your little one through this tough time in your lives!