How to add through-hole pads within polygon pads in Eagle?
Unfortunately that's just the way it is. The polygon inside the package doesn't count towards the ratsnest. If you think about it you haven't been able to give the polygon a name or assign it to a pin in the schematic symbol, so how does it know what net it is part of?

What is special about polygons in the package is that as long as the polygon is not shorting pins of more than one net, it won't cause a DRC issue, even though it is not part of a net. Also it won't be cut away from the copper (it will stay filled in the exact area it is drawn).



As to the solution? Well, you have several options.


Connect all the ratsnest up with wires. Tedious I know, but there you go. This is probably the best option as if you join all the wires with a direct line (not the auto-45 degree or 90 degree option, but the straight line), then the lines will follow the package nicely as you move it around.
Don't add the polygon in the footprint, add it in the layout editor. A bit of a pain as you have to remember exactly where it goes.
Add it in both. You get the copper in the package of the exact shape required, and then you can add a polygon in the layout of an arbitrary shape which covers up all the ratsnest area without having to worry about getting it to be the correct size needed.
Ignore the ratsnest lines. Actually, don't, number 4 is a bad idea...