While it sounds like a very stressful day, I am very surprised that the LGA-DAL-SEA itinerary is even considered a legal connection. Looking at the schedule, if you flew yesterday, I can surmise you were on the 11:20 am flight, scheduled to arrive at 2:29 pm and connect to DAL-SEA leaving at 2:50. It appears to have arrived in DAL 13 minutes late, which would have been just enough to totally kill your connection. Even if you were on the crack of dawn LGA-DAL (which it appears you weren't, since it arrived early), the scheduled layover there would have been only 26 minutes before going to SEA. I guess 20 min is the MCT, but still too close for comfort in my book for any flight originating in LGA.
I guess these very tight connections will all be a moot point once AS drops this route...