Strollers and car seats do not count toward the 2 free bags.
Just as a side note, I recently returned from MCO on a Southwest flight. My checked hard-sided luggage was damaged somewhere between check-in at the airport and the baggage claim belt. Our bag was in perfect condition and working order when we checked it in at the airport. When we grabbed it from the baggage claim belt, the recessed handle was broken at the bottom and a piece of it was missing. They do not handle checked luggage very gently, to say the least! So, you may not want to check them. You might want to gate check them instead.