BRNR, I had to shake my head over your h asking for something from you while he is out on the street. I would tend not to give him anything until he coughed up the funds for his obligations to his children. But, that's just me.
If he's living w/the ow or has a place of his own and she's coming around, he should be able to go out and purchase items for his own place. After all, he walked out and wanted his freedom to do whatever. This is where they have to learn how to live on their own w/o "mom" being there to take care of everything. It's like when a child threatens to runaway and then goes outside and hides in a tent. They soon learn that all of those frills at home were actually quite good and come back inside. Your h needs to come to that realization at well.
I will caution you on this...if you opt to give him the item, it will open the door for him to continue requesting things from the home. The question is...do you want to set the boundary now or wait until all of the cows have gotten out the barn? By setting a boundary doesn't mean you are destroying your changes of reconciling, it's letting him know that you aren't a fool and some day, he will respect you for that decision.
I still have hope for your situation, but I still wouldn't sit around and wait on him. I would continue on w/my life and enjoy the time you spend w/your children. You can move forward and enjoy life and still leave the door ajar. You will know if and when you are ready to call it quits.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.