Should I use a pen name for my children’s books since I want my real name for a different market?
In general, I think that it is a good idea to keep separate areas of your business under different pen names, but there are a few ways to go about it.
If all of your books are going to be the children's books except for the one book that you use as an ultimate business card to promote your own business than it probably is not a very big deal if you use the same name for all of your books. If you think that you might have other business books, however, then I would either use a pen name or use a middle initial or something similar so that it still your name but you have a way of separating them out in the search results. That way if somebody goes to your Amazon Author page, you will have all the children's books under one version of your name and all of the business books under another version of your name.
If you are going to write in multiple genres and the audiences for those genres have a good chance to overlap, you can get away with using the same name. If they aren't a very close match for the type of reader, however, it's probably a better idea to use pen names so that Amazon will have an easier job promoting your books to people more likely to purchase them, which will in turn lead to them promoting your book more.
If you don't want to have books from different areas associated with each other even from an intellectual level versus just from the author's pages level, then I would use a completely different pen name. For example, I know somebody that has a series of children's books and also has a series of dark horror books, and he does not want the kids that are reading his children's books to be able to find a his horror books because they're meant for adults. In his case, he uses a completely different pen name for his children's books.
It really comes down to your own comfort level and how closely you personally want to be tied to any particular series or genre of books.