So much of this sounds familiar, no matter how many times people tell you it is hard to stop these feelings.
Remember that old MN saying, comparison is the thief of joy? You're comparing yourself to a standard which I can assure you, very few mums live up to. If my best friend listed out everything you're dealing with, and then said she was a shit mum, I'd give her a massive hug and a head wobble. You need to be a best friend to yourself and absolutely TELL OFF that horrid little voice in your head telling you that you arent good enough.
You have a job you can't resign from, you're a mum of 3. The job description is massive, you're on duty 24 x7 and when you're sick, guess what you still have to go to work anyway. Or, if you're "lucky" someone will take pity and help out for a few hours by babysitting the kids so you can nap. As if magically that two hours of nap time is supposed to fix the YEARS of accumulated sleep deprivation!
Two things revolutionised my thinking with DS2. For some reason it finally sunk in that it doesnt matter if I'm the best mum ever or not. I'm the mum my kids have got, and if I've made mistakes well, I'm hardly the first mum to have got something wrong.
There are some truly awful mums out there, who abuse their children, and if you're falling into that bucket you need to seek help urgently. But I assume you're not. In which case I can assure you that you are doing fine.
Kids are incredibly adaptable. Your 3 yo and 8 yo really won't suffer lasting damage by you "hiding" from them during your pregnancy. Children live in the now.
Put the baby in a sling, and spend time with the kids looking at the world from their point of view. Life is a lot more fun and simple when you look at it like a child would. Us adults, we complicate things a lot.
Let the housework go for a while. Tell Christmas to F off! The kids will be happy with a stocking full of chocolate and a few games. I can assure you that a morning spent rolling around on the floor in PJs playing games, a stomp outside in wellies after lunch, and a family movie woth hot chocolate in the evening will be enough to make their Christmas perfect.
As for looking crap, not exercising and missing the old you... hmmm I can't solve that one. I am STILL a mess and my youngest is 3. I think I'm now a hopeless case. I so want to do better, but it is hard to find time. I also put myself last, and I know it isnt a healthy thing to do.
The best thing I've done is take up gardening - it is such a fantastic hobby, gets me outside working and the kids love to come out and play. Rubbish in winter, I miss being out in the daylight.