Looks like the eSearch widget will let you select a sub-set of pre-selected entities by feature layer, and the selection widget will let you select all features in one layer that intersect another.
However, if it falls within ANY features in the intersect layer, it will be selected. Does not appear to only find features that intersect the "selected" polygon.
Since you didn't say if you were using compiled or uncompiled and were asking " (or another way to do this) " I thought maybe you were interested in some coding to do this. Thought you might be able to glean some of the select by extent/graphic information from one of these widgets. Maybe have a definitionexpression or where clause attached to your widget that only loads the "selected" polygon and passes that to the selection widget code. Not sure how to do it or if this would work for you, just tossing out some "ideas".
R_