Play therapy is a relatively common from of Psychotherapy and while most Psychiatrists probably aren't trained to use deliver it there are certainly many who are.
My concern about your situation is that your Psychiatrist is not following your wishes and that you appear to be experiencing distress. No therapist should be causing a patient harm and it is inappropriate for your Psychiatrist to go against your wishes. If you are in a situation where you are complying with his direction due to a power imbalance then you may wish to consider changing therapist. Obviously I don't know the details of the therapeutic relationship but it certainly sounds like you are unhappy with what has developed.
Have you considered changing therapists?
It sounds like his proposal is a reasonable strategy, whether it works or not would depend on a variety of factors. Regardless, the issue is still whether you are being forced into an experience you don't wish to have due to the present power imbalance. Regression type therapy certainly isn't the only treatment approach to trauma and it isn't even the one that has the most evidence for efficacy. Cognitive Behavioral Therapy (CBT) is a recommended trauma therapy and it may be something you find much more tolerable as a process.
The way to discuss all of this with him is to do just what you have done here - provide a concise and clear explanation of your concerns. It is actually the therapists responsibility to sort this out and if he knows you are dissatisfied then he is ethically obligated to remedy the situation. Given that you have difficulty with erotic transference with (perceived) powerful males then it may be a much better idea to be consulting with a female therapist so that this issue does not impede your trauma therapy.