Don't openings from the garage into the house need to be elevated from the garage floor by at least one step and have a fire rated door installed? (we were told we could not make a flat entry into the house).

The door at the bottom of the stairs going into the house would be fire rated. May be why that works.

If you look at the second drawing, there is a note for a 4" step up. The door into the house proper is 20 min rated too. I don' see anything (or if there is) a door into the basement but the OP says there is a fire rated one. I assume these plans were approved by the AHJ.

The biggest concern is how open that stair is as you enter and leave the house. It has to have something in front of it because the house entry and basement stair entry share the same landing. It is very tight. And scary to look down those concrete steps at the entry to the house having 4 kids that never calmly walk through any door, I just have visions of them pushing each other and someone falling. If the house entry and the basement entry were in different places this would not concern me as much.

when you stand on the landing to enter the house, to your right is the open stairs

Beyond adding a gate, install an entry door that is hinged on the right and opens out. That would block at least part of the stair opening, although I don't know if it meets code.

Kids are usually a lot smarter than we give the credit for and sometimes parents, naturally, worry about things that really aren't a problem.

If you haven't built the stairs yet, you may be able to rework them so that they turn at the top and are accessed parallel to the kitchen door, leaving a railing where the start of the stair currently shows on the plan (see drawing below).

Granted winding the first three risers/treads may make it tricky moving things in & out of storage, but with two people, I would think one person could hand bulky items over the railing to someone already on the stairs. You can use a child safety gate to assure that the kiddies don't fall. Although, with the turn, I doubt they would fall far.

Just for the record, I patched a couple of pieces together here for the sake of conversation. Had this been a part of a plan for a client, I'd have started from scratch and worked out the details. :)

Thanks to everyone for their thoughts and advice. The stairs are built and we settled on a half door at the entry. Should work out just fine.

You have created a death trap. If you have a gas spill from a lawn mower or other source, the vapors will fill the stairwell first and the 4" step to the basement might not be sufficient so fume could just hang there. When someone opens the door from the basement, those vapors could flood in, find your water heater and blowup. The step from the garage floor up to the house allows the vapors to sit on the garage floor and seep out around the garage doors. But you have defeated that safety factor by putting a "well" in your garage floor. If I were you I would immediately consult an AIA Architect for a solution. The half door MAY have saved you if it is vapor tight but that seems doubtful.