I started homeschooling my second grader this year for the first time! I also have a 2 year old.
I was VERY pregnant, and delivered my 3rd babe on October 12.
So, I was in the same boat as you, and I can honestly tell you, it was the very best decision I have ever made. It is so much easier to keep them home, even when pregnant and caring for a newborn. A newborn babe is happiest at the breast, so I did most of her lessons like that. We did some reading on the couch, I relaxed about what time "school" should start, basically I was just gentle on myself and kids. We took a 2 week break when I delivered. I was worried it was too long, but now at the end of the year, I can say I'm so glad I took it! My baby is now 6 months old and still fits right in our homeschool. Just try not to drive yourself crazy with a tight schedule, allow yourself to rest when you need to, love those beautiful kids and marvel at how lucky you are! You will not believe how much the older ones will still learn. I figured life was wonderful, especially new life, and the best way to learn IS in real life. I spent all summer wondering if I should begin homeschooling with a new baby on the way. DH and I want a big family, so we would never have began if we kept waiting!
You can do it, and you will love it!