Hi OP,
I've just found your post while looking for a thread someone mentioned. Sorry it hasn;t been replied to for a few days. Bet that doesn't help either.
First, I think it is really really good that you are doing these things, even mechanically, while they feel like they are doing no good. Because you might be feeling a lot worse, with a very ugly commentary running in your head (Look at yiy, can't even get dressed, getting so fat, unable to fight it, giving in all the time' etc) if you didn't do what you are doing. And for your children;s sake, and the sake of your relationship with them, being up and dressed and out in the world is massively beneficial. So even though you don;t feel it;s making a difference, I am massively impressed and want to reassure you that it is.
Can I suggest smething that helped for me and I try it whenever I feel depression taking hold.
Do something every single day that you have never done before and record it in a notebook or laptop file. Say what you did and what you thought of it. If your motivation is low, start with easy stuff - try a different flavour of tea or coffee, walk down a different road on the way to work or school pick up, play a song on Youtube by an artist you've never heard of. Buy a different scent of bubble bath or clothes wash. Try a fruit, vegetable or flavour you;ve never had before. Cook a new recipe.
Don't worry if you feel the effects straight away, but gently encourage yourself to get a bit more ambitious with the new things. Try a new exercise class (you don't have to sign up for the lot - just go to one) Stuff I tried included zumba, kayaking, vinyasa flow yoga, body combat, kettle bells etc. I still do some because I love them and others were one offs.
Then add some stuff you've always meant to do but for no reason not done - visiting local landmarks or having a go at a craft. I did some London sightseeing I'd been meaning to do since my teens - climbing Monument (lovely views) and going to the candlelit museum.
One way to do something new is to say 'Yes' to stuff people suggest without thinking too much. Just give stuff a go - new work projects or a weekend away with the girls etc.
I think we get into ruts neurally and doing new things activates new neural pathways which help get you out of that Groundhog Day feeling you describe of 'stuck reliving the same day over and over for no reason only to do the exact same the day after'. (If you haven't seen Groundhog Day - it's a great film.
I'm fighting off a serious depression right now but it's the new things I do rather than the old favourites of exercise and meditation etc, that really work best for me. What you describe sounds like anhedonia which I get and is one of the more frightening forms of depression: just no joy in anything. This really is a great way to combat it. Don;t worry if you feel nothing at first. It took me a while but I kept a diary of 'new things' and after about a month realised i was starting to enjoy some of them, add some to my life, look forward to some, get DC and DH to join in with some and bit by bit the world came back.