J.S.
Sounds like the glider you tried did not have a wide-enough base, or the wood was too "thin" to keep it stable. It's like any other piece of furniture, "one size does NOT fit all". Keep looking....I'm sure you will find a glider/ottoman that you DO like! Keep your eye out for "moving sales" or log on to Craig's List, Freecycle, or e-Bay.
A traditional rocker will "walk", and you will probably find your walls and baseboards "nicked" and "chipped" from when the rocker hits it, and I can tell you from experience with 2 boys that you will NOT want a chair that does NOT rock!!
I loved my glider, but it was a hand-me-down, and I'm not sure how many children it had been used for before it got to me, but it just got too "rickety" for me to be able to keep anymore.
Congratulations on Baby #2!
~J.~