Well, I have to agree with Centerline, but I'll add a few thoughts based on my lifetime of sailing and my present boat, a 1979 DS II.
I was virtually born into sailing, my Dad had a 15'9" BEETLE FALCON sailboat when I was small. The Falcon was a near copy of the O'DAY Osprey (and I am convinced the Osprey was actually a Falcon with a slightly modified deck). By the time I was 4 years old our family had increased by 1 when my sister was born. My parents must have felt that for comfortable family sailing we needed a bigger boat, one with a cabin (and head?) since my sister never went out with us on hte Falcon. So, in 1970 we purchased a new boat, a 1970 CAL 21 (similar to the Mariner). We sold that boat in 2008 due to my Dad finding it better to go sailing with me on my DS II. Anyway, the point is...... You may find the DS II to be a good learning boat and I sure enjoy mine!! However, with your family, the DS II may not be really ideal. The 1982 O'DAY 19 will be more stable, has a small but useable cabin with room for a port-a-pottie and a small bunk area where your 2 year-old can nap. The cabin will provide a place to change into and out of swim-suits, and to stow a cooler. If you desire to spend any nights aboard with more than just you and your wife, or yo uand one child...... (or unless 2 people are willing to sleep in the cockpit under a boom tent?) the 19 may work fine. But, I might suggest that you keep looking and search out a MARINER (1962-78), at 19'2" it is about the same size as the newer O'DAY 19, but the 1969-78 models have 4 bunks inside the cabin, the older 1962-68 models have 2 bunks inside and the cockpit could be used (might require a bit of "backpacker" inginuity) to sleep 2 more. The Mariner is a centerboard boat like the DS II, but like the 19 (which is also a centerboarder) the Mariner has inside ballast to increase stability. The Mariner's CB is cast-iron (165#), the 19 has a fiberglass CB of about 52#. Inside lead ballast is 200# in the Mariner, 300# in the 19.
As I say, I LOVE my DS II, but think you would be better with the 19 (or a MARINER) for family comfort. Also consider a 192, which has a cabin like the Mariner, but is styled like a bit bigger boat. Downside to the 192 is that with her keel/centerboard design she draws more water which will slightly affect trailiering and beaching, Also since the oldest 192 will be a 1985, newest a 1989.....price will be higher than for the Mariner or 19.
As was said above, we can comment on the 2 models that you mention, but for true test....yo uneed to find someone local that knows boats and could come with you to help look at the boats and perhaps provide a knowing view of each boat's condition vs price.