We used to struggle to hire a role of UX designer after our product was launched. As a result, we decided to hire a UX consultant to give us advice/suggestion to improve our user flow and product. To be honest, we failed to practice the UX methods and testing. We ended up adding a lot of unnecessary features into product.
My suggestion is to hire a full-time/in-house UX expert if it is affordable. You could find UX designer in Linkedin or UX community forum.
An experience UX designer should know all the skills:-
concept design, adaptive design, marketing, user testing, user metric, user research, etc. Personally speaking, development(coding) and human psychologist are good to have too.
If an UX designer has a skilful, he will know how to find a way to test in the kids apps. Of course, it is a good mark if he has designed a kid app before.
If your budget is tight and it is not easy to hire one immediately too, meanwhile, you can define the user story and user scenarios to help you make decision what features should be developed. Before developing it, test the ideas and concepts with kids by using a quick prototype.
You can use these prototype apps (Marvelapp, Invision and so on).