OP, your husband is most definitely an abusive narcissist.
We have a thread for victims of narcissistic abuse; it's often family members but also partners and ex's.
Every single thing he has done is part of the script for not only a guy wanting out, it's typical narcissistic abuse.
Gaslighting you, lying, little to no empathy for you, no accountability, trauma bonding you, hoovering you back in with bullshit threats of suicide.
If he was that suicidal he'd just do it. That I am sure of. ( I've lost loved ones to suicide). This for him is a manipulation technique.
These people have a personality disorder. It is fixed. Therefore, declarations of change etc are never genuine. The change is always temporary. It is impossible for them not to be CFs and they ALWAYS revert back.
Your best bet is to continue therapy. I've had 15 years worth to try understand narcissistic abusers in my life.
You are trauma bonded to him so will believe bullshit lies and feel comfort in him ' coming back to you '. I can assure you, this relationship will never ever be good for you mentally and physically.
Get yourself and those kids out of this.
He won't want 50/50 for long even if he does get it to begin. The threat is to instil fear in you. It's a narcissistic abuse technique. The key techniques the cuntfucks use are FOG ( Fear, Obligation, Guilt). He will pull every one out the bag.
God you deserve more than this.
Dr Ramani on YouTube gives excellent advice on dealing with narc abusers ( yes he really is one). Your therapist hopefully is familiar with this too and could advise you.
Never ever go to joint therapy with him.