Hi Kalina!
What a wonderful trip you are planning for your family and I am sure the children will be beyond excited as the time draws near. You have chosen one of my favorite moderate Disney Resorts,
Port Orleans Riverside. All of the Disney Resorts will have a specified check-in and check-out time. Check-in time for the Disney Resorts is 3pm and for the Deluxe DVC Villas it is 4pm. If you arrive before that time you can request to receive the first room available. That might mean your initial request to be in a particular building or room cannot be honored so that is the risk you take.
During busy times of the year when the resorts are full they need all of that time to clean the rooms and get them ready for the next guests. Since you are arriving in March this might be a spring break week although it is always hard to know ahead of time as schools change calendars from year to year.
Getting a late check-out follows the same rule. Check-out time is 11am and again during busy times they must adhere to that time to allow the rooms to be ready for the next guests. You can certainly ask for a late check-out but if they can honor one it is usually just an hour.
Each resort will have a bell staff that can store your luggage before and after your stay so you won’t have to worry about lugging it around with you. Some things I recommend is that you bring the children’s swimsuits with you in your carry on bags so you can enjoy the pool while you wait for your room. You are welcome to enjoy all of the resort amenities on check-in and check-out day. You can do the same the day you depart. You can also store your bags and take a bus to
Disney Springs and enjoy the dining,shopping, and entertainment that is there.