Loving a child & being able to care for a special needs child when there are other relationships that need to be nurtured & maintained (spouse, children, other family member needs, etc.) can cause a lot of internal conflict. On one hand, you want to do everything possible for the SN child, which takes a lot of your time, energy & emotional output. On the other, you want to be able to give just as much to everyone else in your life (& rightly so).
I know many years ago, there were "institutions" that families could turn to. Now, it seems the help has changed towards offering programs & in-home assistance. But there are still residential programs for children & adults.
The site I'm linking below is for a facility that offers residential therapy, & seems to be child-focused. Letting your child live outside of your home may not be something you & your husband are comfortable with, or perhaps even considered. In addition to this, the site also has a wealth of information available through links to programs, FAQ's, etc. that may offer help.
You didn't mention what type of care assistance (if any) you have for your son, but it's possible that Medicaid would be something he qualifies for, which could open doors to in-home therapies, developmental programs & care-giver relief for you & your husband.
As for your relationship with your husband, I think having 'tricked' him into therapy may have damaged trust between the two of you. It sounds like he is unsure of how to proceed as the father/husband/head of household in your family, and instead is taking things one day at a time, which doesn't give him any "light at the end of the tunnel".
It sounds like (& I'm not saying this IS what has taken place) you are asking him to follow through on things that you find helpful, & are disappointed when he rejects those as viable solutions for him. If you haven't yet, ASK your husband. Something along the lines of:
"I know we are both overwhelmed. I want us to get into a good place, as parents, as spouses, as friends. I find it helpful to XXX, what would be helpful for you to feel like you are doing more than just surviving where we are at right now?"
Maybe he would be more comfortable finding support in a group of other parents going through similar trials, or talking privately with someone from your church, as opposed to a therapist. (Therapists can come with assumed stigma, & not everyone is comfortable with the thought of needing to talk to someone professional, or taking medications for situations).
Be supportive. I think pointing out that he 'blows steam' & threatens divorce is helpful to redirect his thoughts to what he truly wants, but try (I know, hard, esp in the moment!) to do it without challenging him to follow through, or threatening him with a bleaker future with the kids if he does. I fear that will only further drive a wedge between you both.
Here's the link to the info above. I hope that you can both get the help & support you need, & can work on making a stable environment for your son, other children & each other, with love, care & nurturing. T.
http://dmh.mo.gov/cottonwood/