You can apply most any finish over shellac but not much of anything stick's to poly. I would use latex enamel so I could repaint as needed in the future.

Lucky you! I did a search and clear polyurethane is recommended:

How to waterproof over shellac

Poly chips when damaged. It is almost impossible to spot repair those chipped areas, meaning the entire area/piece has to be refinished. And, of course, the chipped areas look funky and no longer protect the wood.

Use paint or varnish(not poly varnish).

And be aware, the water will degrade the bottoms of the rockers/legs. Applying finish to those areas will help protect, but the rockers will wear off the finish in use.

Thanks for the help, everyone! I appreciate it. I know what I'm doing this weekend! :)

I repair old furniture as a hobby. If it was put together by hide glue (quite likely) the joints will fail. Animal hide glue softens if exposed to moisture.

I'm going to need to get something on mine too!

I would worry about them "walking off".

Can we see pictures of them?