Welcome to Kansas City!! I know it can be frustrating and a little scary when you move to a new place and dont know the area well. Especially when you have children and are trying to get them adjusted as well!
My daughter goes to pre-school within the school district. I am a stay at home mom but it is great for her to get out and be with other children and we have loved her teachers and there are plenty of opportunities to meet the other parents and children your son/daughter comes into contact with. They encourage parent involvement and really allow us to be active in the parties and field trips. They are very safety oriented, they have a great playground and my daughter loves it and has really seemed to blossom there. They have a lot of different time options, some may be full now because the new school year just started but they could put you on a waiting list.
It is the Park Hill School District, ###-###-####.
I hope that helps, if you have any questions you can email me. I would be glad to share any other info on the school. We live in the Parkville area so we are not that far from you.
Good luck and again, welcome to KC!