please tell me how to find children's animation production companies

Also, how do I search for management companies that handle children's writers?

Hello @cormo,

Unfortunately, we don't have these specific search parameters.  However, we have updated the post to an "Idea" so other community members can vote/comment on this feature improvement and staff can monitor to gage interest.

In the meantime, as a workaround, we encourage you to instead perform a specified Advanced Title search for animated & family titles, you can then have a list of children's animated titles and can explore them for the listed companies to create your own list of companies: https://www.imdb.com/search/title/?genres=animation,family

About your second question, likewise, you can review the title pages from that search to find the listed writers and can identify the management/representation by looking at the IMDbPro pages for those individuals.