How to leave house owned prior to remarriage to my children? 

There are a few approaches to this, assuming you are the only owner of the house (on the deed).  One of these would be to simply leave the house to the children at your death, which would be entirely your right, so that your new husband's financial problems would never have a chance to reach the property.  However, you should talk to a wills and estates lawyer, since a surviving spouse has a right to a certain minimum portion of the estate, no matter what the will says, and depending on your other assets, this might cause a problem.  Another approach might be to put the house into a trust while you're still living.  There are far too many things to consider, here, and too much at stake, not to do this the right way, with professional help.