I think he should have access to his children as requested, provided he can provide a minimum standard of care while he has his children with him. Yes, that includes feeding them in time, and not getting drunk when he is the only responsible adult around, btw. However he can happily plug them to the xbox all day and SS wouldn't bat an eyelid.
You don't have a right to control what they do when they are with him. Or to choose when new people is introduced to your children. But you can object to visits that are in detriment of the child. Contact taking place in a shared house is not one of those things that would advance your case.
As for maintenance, get the CSA into the case ASAP.
And most importantly, get some support for yourself, you need to stay strong for the sake of the children. And need to move on for your own sake.
Many years ago, when the ex and I went separate ways, a person from the Centre for Separated Families told me the following when I mentioned I have offered to babysit DS when the ex wasn't able to care for him due to his multiple social/work commitments: "At this difficult time it is understandable that you want to keep your child with you most of the time, but you do also need some space to get your strength back and rebuild your life."
She was very very right. Those little breaks when DS went to his dad where used to lay the foundations about what my life as a single mum would be, it helped me to get myself organised rather than overwhelmed by the new reality of being totally on my own. With time you will be able to take on more time with the children or let them go for longer, but that is another's day battle.