Frog......have you considered consulting a therapist for your children?.....as that would, also provide a paper trail and documentation, that could be important should he force this into a court conflict....
***If you do so, be sure to mention that he he has discussed his suicidal ideation, on many occasions with you...as well as his physical appearance decline and hostile attitude ...especially, in front of the children.....
I am with Trailmix, in wondering if he is not drinking during the week, and trying to stay sober only on Saturdays.....What makes you thing he is staying sober? Just because he goes to AA meetings, does not necessarily mean that he is staying sober......some people actually go to the meetings while intoxicated....
If you are not satisfied by the guidance of your lawyer, in this respect, I suggest that you consider calling the local dv center and ask for a referral to a lawyer who has lots more experience in these kinds of visitation issues....