Mom with Alzheimer's will take her cup (that has a lid and straw) turn it sideways and move it back and forth. Any advice?

Mom does these things because she has Alzheimer's. We can't begin to understand what's going on in the mind of someone with Alzheimer's. If the ice cream thing is getting to be a little messy try putting out an empty bowl and guiding her to plop her ice cream into that bowl instead of right on the table. Bless you for caring for your mom. Alzheimer's is so wicked and so awful. There's just no other disease like it.

With the cup, perhaps the movement and the color fascinates her when she's moving it back and forth. Maybe you can buy her a colorful soft ball to play with? Roll it on the table to her, so that she can roll it back to you? It'll also make a good exercise for her - eyes and hand coordination.

The spoon and ice cream.. I don't know about that one.

Each person going through dementia experiences something different from others. Not all are alike.