How to get parent who has been verbally diagnosed with Alzheimer’s into a hospital for evaluation?

I don't think you can. She will only be admitted when she needs medical care.

What is the purpose you think it would serve to have a hospital evaluation?

If you are looking at what type of care she needs, a neurologist can be helpful or you can contact your local counsel of aging and they will help you get an assessment for level of care.

I am sorry that your family has to travel this journey. It is a difficult one. Remember, it is a marathon not a sprint. Hugs to all of you.