Gossip and nastiness are everywhere Jess. What has already happened is bad enough, surely you don't need people talking behind your back. There are always people who enjoy other peoples misfortunes (unfortunately) but I don't think that should be a deciding factor in leaving your home. An article in a newspaper cannot hurt you compared to what has already happened. Your children are young enough that if you explain to them simply (with not too much detail) and honestly what is going on, they probably won't get too upset about it. As their Mom, if you are outwardly not too bothered by the gossip, they won't be as affected by it either.
With that said, if it something that should not have been written about, your lawyer should make sure that it does not happen again.
It seems as if when things can't get any worse - they do . I hope you can get through this with your head held up proudly. Remember - you are not the one who did anything wrong in this case.

Kathleen