My situation is a little different from yours. My OH also works very long hours. I'm a stay at home parent and homemaker. You didn't mention that of yourself, but with those long breastfeeding milestones, I don't see how you could work outside of the home and manage that. Wow! I tried and started to dry right up!
Anyway, when I had my third-born, my others were 2 years old and 11 months old. So having two babies was the real kicker, and my 11-month-old wasn't walking yet and was still nursing. Besides that, the early days were just the same as any other time. A focus on breastfeeding, heating up lots of freezer meals I would put together twice a month. Lots of time spent reading and snuggling with my kids. An absolutely filthy house for a few months. Haha. This might be similar to your situation depending on how many additional needs your 2-year-old has. I'm not sure!
When I had my fourth, my oldest had just turned 4, so my others were 2.5 and 1.5. This is closer to your age group. It was a ton easier, too. I had already been through the "I'm out of hands!" Phase that I went through when my third was born, which really wasn't a difficult adjustment. My 2 and 4 year olds understood better about what was going on. My oldest was a huge help, and all of my kids love babies and siblings and want lots of both, so there's none of the problems associated with when some kids don't want little siblings or get worried about losing their status, if you know what I mean. I had it easy. My baby still nursed a lot in those first few months. I was running in little sleep. I think every newborn stage has been very similar. But having kids who were old enough to fetch a diaper or hold their little siblings' hands when we went out was a wonderful asset.
You can do it. It's okay. It's not scary. It shouldn't intimidate you. You'll lose your mind, but you'll get it back when your kids are grown. I think. I haven't gotten there yet.
The biggest issue is leaving the house. When I took two kids grocery shopping, they'd run off in two different directions to go look at stuff. Now, I have three who are easily distracted and will rub off in three different directions. I do bribe the kids with candy when we go shopping, we try to shop at places where I can put 2-3 kids in a cart (I wear my babies) and give them each a snack I've packed for them while I do my bi-weekly shopping. We still go out and do fun things. We are all very close. They are all very wonderful and usually very well behaved (unless I go grocery shopping close to nap time. That's when we have running off.)
I am thrilled for you. Congratulations! Having three is a game changer, but my third born is so completely awesome. I'm so thankful for her.