How can I get my aggressive mom (who has dementia) in a nursing home?

Has she been diagnosed with dementia by a doctor? Do you have Durable Power of Attorney and Healthcare POA? If not, you might consult with an Elder Law attorney in her jurisdiction to see what steps you can take to get Guardianship and therefore, the authority to act on her behalf, place in her safety and manage her finances.

IF you do have DPOA and Healthcare POA, I'd likely discuss your concerns with her doctor. Likely, you'll need to get documents in writing that substantiate that she is incompetent, so you can step in to handle her affairs. It's not very easy and would be difficult to do from 2 hours a way. You might explore the services of a Geriatric manager to help, if the funds are available. Resistance to care is quite common with people who have dementia and sometimes, it's difficult process of seeing what will work. I'll bet you get some good suggestions on this site though.

How advanced is her dementia? Is it unsafe for her to live alone? If she won't go, you might have to get the someone involved that can determine her condition and maybe she can be forced into a NH, if she really needs one. Do you have POA?