I work from home full time as an editor/market analyst. It used to be an office-based position, but about a year before my oldest child was born, they started letting everyone except sales and management work from home. I shake my head when I think of how easy my life was back then, working from home with no kids!! It got harder when DS was born, but he was a reliable napper, so I could count on getting at least 3 hours of work done during the day, doing another 3-4 in the evening after DH got home, and then catching up on the few extra hours over the weekend. It felt hard sometimes, but doable.
Then DD was born, and it's been so hard since then. Having 2 kids in the house is just a totally different dynamic, and DD hasn't napped at all since she turned 2 (and even when she did, DS was still up so I couldn't really work). I get up by 6 so that I can get an hour or two done before the kids wake up, but I pretty much can't work at all between 7am and 4:30pm, when DH gets home. Very rarely I'll put on a movie for them in my bedroom while I get a tiny bit of work done or at least check e-mail, but the bulk of my work gets done during evenings and weekends. I try to prepare dinner during the day so that it just has to be stuck in the oven or something in the evening -- that way I can go upstairs and work right when DH gets home at 4:30, work until dinner is ready around 6:00, come down and eat, then go back up and work until 9. So on a good day, I've gotten about 6 hours of work done by the time I go to bed, leaving 10 hours for the weekend. It's not ideal, because it feels like I never really get a day off, although on weekends it is nice to be able to work when I'm fresh and alert instead of when I'm wiped out from a long day with the kids.
A huge part of why we're able to make this work is that my DH is happy being the main caregiver any time he's at home -- he walks in the door and is instantly engaged with the kids, playing with them, doing the final prep on dinner with them, and then after dinner doing the wind-down routine with bath, stories, and putting to bed. He totally gets how hard this is, and even insists that I take one evening a week off and go out and do something by myself, like browse a bookstore or get coffee with a friend (and I insist he do the same -- usually he chooses to go for a long trail run with a friend on those days). I think both of us feeling appreciated and supported really helps -- we feel like it's hard, but we're a team and are in it together, instead of feeling resentful or like one of us is shouldering a much heavier load.
I definitely have days where I melt down, saying that it's unreasonable to expect this much from me and generally complaining about everything, but those days are few compared to the ones where I'm grateful to have a flexible schedule, to be saving zillions of childcare dollars, and to get to be with my kids all day. And this fall my DD is starting preschool, so I feel like we've "made it" to the end of the really difficult part of this. She'll only be in preschool for 7 hours a week, but it's amazing how productive I can be now that my time is so precious -- I bet I'll get tons done during those 7 hours since I'll be alert and undistracted, and my evenings and weekends will open up a tiny bit more, then even more next year, then the year after that she'll be in kindergarten and I'll be a free woman on evenings and weekends!!
Wow, that was long, sorry! Good luck to you -- the fatigue in the first trimester is so difficult to get through, especially when you're trying to use your brain in any meaningful capacity in the evenings. Maybe something like a mother's helper would work for you -- having a young person come in for a few hours a couple times a week could really make a difference in how much work you'd have to do after-hours. I always meant to look around for someone like that, but never got around to it. Another idea is, if you're friends with any other SAHMs in your area, you could set up a little co-op, where each of you watches all the kids for a few hours once a week. Of course that won't work with a tiny infant, but it could be useful right now, and again once your baby is older.