I would say go to the gym if your dh is saying he'll look after the kids. If you enjoy it, then that is part of the way to having fun in your life again. I understand totally how you feel about getting out with your children. Sometimes it was too much for me to get out of the house, as I used to panic about being attacked when with ds, and not being able to protect him, or having an accident, and leaving him motherless and crying in his pram.It sounds ridiculous to those who have never felt like that, but it is a very real fear. My dh used to tell me to go out, as he knew that the exercise would help me feel better, and I know that I felt a sense of small achievement when I did manage to walk out with ds, even for a few minutes. It's funny, because I was OK if I was meeting someone else, but felt panicky if I had to go out on my own.
I really feel for you, and don't know what to say to help you feel better. I know that telling you to go out with your children might make you feel even more inadequate, as you already know that they need to get out in the fresh air. Believe me, I am not judging you. Can you meet a friend in town for a coffee, with your children? Can someone trustworthy look after your 4 year old, to let you spend some close time with your 1 year old?
I am on Cipralex, and it seems to be working, except for PMT, which I hope will be gone soon. I think that I am on 10 mg. I haven't heard anything about your pills, but they usually take about 2 weeks to a month before you notice a change. I have tried loads of others, but nothing touched my last bout of depression in 1998-2000. I think that I had let it take hold too strongly before seeing the doctor. This time, I got in fairly early, and I hope to be OK to come off them in the minimum period of 6 months. We'll see. Anyway, I am still here if you need to talk.