Yes to all of the above. If you check-in online there may be some blocked seats that are available at check-in. If that doesn't work, try the counter and if that doesn't work try the gate.
Welcome to FT! Good luck with the seats.
And if that doesn't work, ask on the aircraft after you have taken your seats. Most people are sympathetic when you have kids. It helps if you can trade a window/aisle to someone who is seated in a middle seat. I wouldn't expect to get 4 altogether, but you should have no problem getting 2 + 2 together.