My mother's husband's children are questioning her ability to care for him, and have accused her of manipulation. Does she need legal help?

Sounds like there is more to this story than you have indicated. Exactly what harm do they see happening to their Dad? Do they plan on taking over his care or are they just trying to take over his money? As far as I know manipulation is not a crime so I doubt APS is going to be very impressed. How much is your side of the family prepared to assist your mother. What step dad says can't be relied on because he has presumably been diagnosed with dementia

Sounds like it is time for the whole family to have a family meeting or conference call on this to straighten out any issues there may or may not be in this matter.

If she can afford an attorney, she should get one, both to protect herself and to make it clear to the accusers that they will be held liable for false reports.

There is simply no way to hold anyone accountable for false reports to APS. APS will never release any information about reports they receive or who they received them from. You will never get the proof.