My children were 6, 3 and newborn during my first year homeschooling. I was concerned while I was pregnant but everything turned out fine. Here are some things I think you should think about:
1. Focus on the basics. For my son's K year we focused on math and reading and just read books and followed his interests with everything else. We spent no more than 1 hour per day on formal lessons, and by the end of the year he was still well above grade level. Because homeschooling is 1 on 1, it doesn't take nearly as much time.
2. You don't have to follow the school schedule. If things are still a little hectic when your newborn is 3 months old, you can just wait another month or two to get started and extend your year a bit further into the summer. In Texas, summer is a great time to homeschool because during the day it's too hot to go outside.
3. I wouldn't recommend putting the 3 year old in Mother's Day Out. One reason I'm extremely glad we homeschooled that first year is because I didn't have to worry about getting 3 children up and dressed and out the door at a specific time every morning, and waking a newborn up to go pick a child up.
4. Do school during your one of your baby's naptimes. Read or do a short activity with your 3 year old, then set her up with a quiet activity. It may help to rotate them on different days. You could give her some workbooks or coloring books one day (we love those jumbo coloring books), playdoh another, puzzles, art activity, etc. Keep them put away until school time so she has something to look forward to.
This site has some really simple preschool activities:
http://www.successful-homeschooling.com/homeschooling-pre...
5. Don't get discouraged if you don't get around to everything you want to do. With homeschooling, you can never be behind because you set your own pace, and because of the one on one attention, your daughter will still get more than she would have in a classroom environment. Also, don't feel you have to do every single activity suggested by the teacher's guide.
We had so much fun that first year homeschooling, even with a newborn. I love that my children we able to be home with him that first year.
Good luck!