No, I don't believe you can make or force him to show emotions. I'll also go out on a limb and say he does have them, but they are buried deep inside. My husband also does not seem to be very emotional. It could be because of his upbringing and possibly because I have so overwhelmed him with my own he buried his deeper.
I feel may alcoholics have lousy coping skills. Coping skills to deal with life throws their way or life so "hurts" them that they drink to avoid the emotional reality.
AA teaches the A to deal with life on lifes terms. This is coping. My husband has come a long way, he is almost 2 years clean and his sponsors and the program has changed his life and mine.
I totally disagree with the therapist who says he is just hard wired to be unemotional ....... get a new therapist. Someone who is totally void of emotions and has disregard for their actions and harm they can do to others is considered a sociopath I believe, your husband does not sound like a sociopath.
You need to understand and accept that he may never tell you about what he has gone through. That belongs to him, not to you. If he wants to share it then great, if not, then you need to accept that, support him in his recovery, do your recovery and grow together. Remember, this is not about you, but about him right now. Go to Al Anon and learn to live your life to the best of your ability. Your happiness does not depend on his recovery or non-recovery. It depends on you.
Accept and love your husband for who and what he is. You can't change him or make him emotional. Yes, in my opinion you are drowning him with your own emotions. This doesn't mean you don't deserve to have them, but what's hurting you is that you want him to have the same level of emotions as you do and he doesn't, at least right now. I hope he continues with meetings after he is home from rehab.