Some things to keep in mind and to bring when homeschooling and going on the road go hand in hand.
Snacks: Since you do not want to go broke buying food but you know your little ones will want to eat pack your own snacks. Be prepared with healthy snacks like carrots, apples, bananas, granola, chewy bars, yogurt (the kind in a tube works very well especially if frozen first), and plenty of drinks. I simply froze Capri Suns or brought a huge water jug and put in the trunk. To entice my little ones to drink I purchased fun animal cups. My older ones appreciated the snacks and water as well after their physical activities.
Games and books: For times I know we will be waiting I bring a tote filled with card games, flash cards, small board games, blanket (for sitting on at the park), and books. This has been a sanity saver!
Activities: I make special activity packs for my two younger children. I simply use a Ziploc bag or a tote bag. You can also use brown paper lunch bags and have your children decorate their own. Another option is housing your supplies in a clear plastic shoebox. Recently, I discovered a clear plastic storage block that was 8.5 x 11, so it is perfect for coloring books, paper, crayons, stickers, etc.
I fill the activity packs with Wikki Sticks or Bendaroos, a small jar of Play Doh, crayons, paper, coloring books and stickers. Magnetic toys and those wooden toys which allow you to dress up the girl or the alike make great take along activities also. In addition, you can find self stick foam activities and supplies at the craft store for a fun boredom buster. They love having their own special pack and it keeps them busy for quite some time.
Change of clothing and grocery store bags: I always bring a change of clothing and grocery store bags with me. The grocery store bags are for messes they will make. This keeps the car nice and clean. I can also use the bags for bouts of car sickness that my youngest is prone to have. A change of clothing is essential for little ones since they are prone to spilling drinks and food and potty accidents.