You deserve a day to yourself every so often. If that can be arranged, do so! You'll feel better for it and it will be something to look forward to. I would have loved that, probably spent the day in bed some days but so what.
Parenting young children is very draining for even the most enthusiastic parent, nothing to feel guilty about and nobody should judge you. Not everyone admits it. That's the beauty of an anonymous forum such as this, we can let it all out and nobody is going to gossip.
I know this will be said to you a lot but it will pass, honestly. Once you're back at work, even part-time, you'll feel better too but your youngest is still a baby.
See what you can do about having a day off - a full day - once a week. In the meantime do look after yourself, your general health is very important. Eat well, healthily, and take a little exercise other than running around after the children. Dance to a video or something like that, it does help.
Many of us have been where you are now and we have survived.
Good luck.