The problem with a trial separation, especially one for only 6 weeks is that you're both still in limbo. As my father used to say you can do anything standing on your head for a short period of time. That is to say you can endure anything especially if you know that there is an end to it.

Today's society has a view that marriage is disposable. That is sad. However, a fulfilling marriage will not work if both parties are not willing to work on the issues. Realistically it's never 50/50 but both parties have to put in some effort. It does not sound like your wife is willing to put in any effort.

Stop apologizing. This is who you are, warts and all. You deserve happiness. If your wife is unwilling to embrace who you are as a person then the relationship will not work. You're very worried about your children, which is wonderful. But children are clever creatures and you are teaching them what a relationship should be. If you cannot stand up for yourself for yourself, do it for them. I wish you happiness and peace.