Delays were my biggest worry as well. Southwest already cancelled our original plans, and with college spring break being a disaster, and us traveling on our kids' spring break, I was expecting the worst. No issues for us at all, though.I just hope the flights are not delayed. The thing that gives me anxiety is all the baggage we're going to have. 2 car seats, a stroller, 2-3 suitcases.. that's a lot for 2 adults to wrangle, in addition to a toddler and infant. We'll manage I'm sure but I'll be ready for a beer by the time we get there
Our two boys are 6 and 8, so they were able to help with luggage. We had the exact same as you, with everybody except my daughter taking a backpack on the plane.
We did Yellowstone when my boys were 1 and 3, and it was really rough. 2 car seats, stroller, hiking backpack to carry the 1 year old, 2 big suitcases, and I believe 2 smaller carry on suitcases. The kids were too young to help. Our flight from DFW to Jackson Hole was cancelled so we had to spend the night. In the end it all worked out - a bit of a hassle to move all the luggage around, but give yourself enough time and you'll be fine.