My advice RT is to NOT make any decisions about that yet.
Your first priority is to get financial protection and support for you and your kids.. addictions like this can be fierce and destructive and you do NOT want to be one of your H's casualties...
After you have financials and some security sorted out then you can make a more level headed decision about the marriage.. its a big decision that will affect your children also...
Whether you can trust him or not isn't the only issue, its can he be a better father IN the marriage or OUT of it?
Kids growing up with single moms have a rough road ahead of them.. if they will be better off that's great but the statistics are showing this is not the case..