Separation, children, and spouse cohabitating

my estranged husband is bipolar, had a panic attack in may that had him in the er, then was prescribed zoloft and klonopin by a medical doctor. he was drinking with his meds constantly, and his lips became very loose. in july he decided to leave the family after having an hour and a half chat with a girl on facebook. the original plan was for me and the kids (ages 9 and 8) to move into an apartment across the street and he stay in our former home so that the transition would be easier on the kids. long story short, he lost interest in the first girl and met another on a dating website 2 weeks later. within a week, he decided that he was moving in with this new girl. (we were still living in the same home at the time) the kids have taken all of this really hard. now, only 2 months after the initial decision to separate, he is telling me that i am being ridiculous because i asked him to spend time with the kids alone. i feel like he needs to mend the hurt he has inflicted on both kids and focus on them if/when he does pick them up. most of the literature i have read recommends that a person wait several months before introducing new girlfriends/boyfriends to their children, even later in separation. he has only picked them up once in our separation, and he did not feed them all day. he also took them over to his new house.
do i have a legal ground to ask him to spend time alone with his children? do i have to let them spend the night there? are there any guide lines for how to handle this?
i hope to get sole or full custody in the future, and he has said he will sign whatever.

There are no legal guidelines on how to handle this. I can tell you that courts will not ever force someone to exercise visitation rights with their children either. So, even if the court ordered he be granted a certain number of overnight visits each year, if he fails to exercise this right, you nor the court system can force him to do so.