My display cases don't work. They just open and close, I can't put things in them, don't get the option.

Yes, they don't function like the ones in the base game homes. I don't know for sure whether this is intentional or it's an oversight by the developers, but in Hearthfire homes you have to just drop stuff into them, which is frustrating because the items often end up on the floor or in other undesirable places. You may have to pick up the item you want displayed several times and try dropping it in again if it doesn't land in the display case.

You pick it up after you have dropped it and put it in the display case, so you should at least have no trouble getting it in there, it is getting it straight some struggle with.

To avoid most problems, drop whatever you want to arrange or put in the display case on the floor, leave the house of go through some other loading door like the cellar door. Return and you should be able to move the item where you want to and it will stay there. Some items you do have to drop in place, most you do not. Put the curser on the item, press A and hold it a bit then used the sticks to move it around, press A again to let go of the item. It is not that hard to just put it in a display case.