Here are some tried and true tricks that worked to keep my toddler happy while my 5 year old and I homeschooled:
* Remember: The first month or so is the hardest, so put on your patience cap. It will get better!
* Keep certain toys only for use during homeschooling. Pull one toy out when homeschool starts, then add another item when your toddler looses interest in the first thing, and so on. You can keep the toys in one box, or you can have one box for every school day. It's vital to choose only toys that your toddler can easily play with on her own. Good choices include play dough and play dough manipulatives, super easy puzzles, blocks, and books.
* Give your toddler "school work." Go to the Dollar Tree and find some coloring- or workbooks. Buy fresh crayons and a special pencil just for your toddler. Then be sure to tell him this is his "school work." (This trick was the magic one for my toddler.)
* Don't completely ignore your toddler. It's hard to juggle the needs of more than one child, but whenever you can break away from homeschooling, even for a moment, acknowledge your toddler. Give her a hug and kiss - and since it's likely he just wants to feel included, compliment the picture he's coloring.
* When your toddler makes it impossible for your older child or children to concentrate, move the toddler to a different location. For example, you could put her in her crib until she calms down. I found that putting my toddler in his room with a baby gate across the doorway worked well. He usually quieted completely once he was there. Don't leave the toddler there indefinitely, if you can help it. One or two minutes is usually all a little one needs. But don't be afraid to put her back if she starts causing trouble again.