Hi F.:
I'm editing my original response based on your add'l information. Thank you for sharing that it's a gambling problem- that puts the whole situation in a differnt category that really wasn't clear based on your original post. You are totally justified in wanting to leave or move on, but you are kidding yourself if you think dating another man is the way to do it or that it means nothing to your husband. Doing so is clearly an F U to him, who you probably loved before he ruined your joint lives with his gambling. Which means you're basically trying to get back at him. I am sure this new guy seems irresistible as a result.
Just a little about me- I too was in a bad money situation caused by my husband that lasted for many years. During that time an incredibly gorgeous guy became interested in me. It's been 10 years and there's not enough time in the day to provide the details, but I know now that whole thing was about getting back at my husband. I just wanted to hurt him because he hurt me so bad with our money situation. To this day I still feel somewhat justified, but it was the wrong thing to do, for the wrong reasons, just wrong wrong wrong on every level. THe f-d up thing is that it seemed soooo right at the time.
Dating will add a lot more negativity to whatever interaction you have w. your husband and that WILL affect your kids. Don't do it. No one needs to "date" that badly. And believe me, another man does not have the answer.
You need to be alone and focus on your kids. Although you're under the same roof as your husband, which totally sucks by the way, you can still live a very separate life and be happy as possible by focusing on your kids. Get out of the house with them as often as possible. FOcus on womens groups in the area.
The LAST thing you need is another man in your life. Last summer I was in a bad way w. my husband. I went on line and found moms groups in my area. I spent every weekend, every spare moment out at parks or the beach on play dates with other moms. It was beyond wonderful- so much more fulfilling than dating could ever be. I highly, highly recommend it. (BTW, am totally available for play dates, please feel free to contact me personally!!)