Maybe step back and ask the question, why do you want to nest a webpart inside another webpart? OR even better yet, what are you trying to accomplish? Are you looking to use some features of one webpart inside another? If so, then you're better off referencing the actual control utilized in the webpart.

For instance, I want to create a webpart that looks up details from a custom table, display selections in a dropdown list and based on the selected index, I populate a list of items from another custom table in a repeater.

I'd create my own webpart, place a <cms:CMSRepeater> and a <asp:DropDownList> on the control page. Then in your code behind you publicly expose properties for the end user to set (TransformationName, AlternatingTransformationName, SelectedTransformationName, etc.).