Hi Lindsay,
Jiko - The Cooking Place is a great restaurant, one of my favorites in fact. The African-inspired fare there is delicious. Your children will be welcome at this restaurant and there will be other children there; however, it is one of the slightly more upscale dining options at Walt Disney World. We just took our 8-year-old daughter there for the first time. You just might want to be prepared to take your 20-month-old son for a walk if he gets antsy. The restaurant is right near the pool and a playground, as well as some places to look at animals, so if there is an adult who is willing to take him out for a while, that might be a nice break. You could also consider eating at
Boma - Flavors of Africa, which is the African-inspired buffet right across from Jiko. Boma offers so many options on the buffet, it is amazing. There are African-inspired dishes as well as a children's section with more traditional American fare. Boma is a slightly more boisterous atmosphere; less fancy dining than Jiko.
Your plan to do the four different parks on one day each sounds wonderful. I am not sure which character meals you are planning on, but if your sons enjoy them, doing one a day could be really fun. I suggest that you try to see different characters at each meal. A final suggestion - if you have some time in your schedule, take time to explore Disney's Animal Kingdom Lodge. You will receive a list of activities when you check in. These activities may include learning to play African drums, hearing African folktales, and of course lots of activities with viewing the animals.
I would love to help you plan more Lindsay; however, I am limited in the amount of space that I have. Please do not hesitate to ask if you have any further questions!