Nanny Tax exemption and Dependent or Child Care Expense tax credit

Hello so if I understand this correctly for 2023 if I hire my mother to take care of our children in my home we are exempt from nanny tax because we are Married and both working even though my children are under 18 according to publication 926.

Wages not counted. Don't count wages you pay to
any of the following individuals as social security or Medi-care wages, even if these wages are $2,600 or more dur-ing the year.

1.
Your spouse.
2.
Your child who is under the age of 21.
3.
Your parent. Exception: Count these wages if both
the following conditions apply.

a.
Your parent cares for your child (including an
adopted child or stepchild) who is either of the fol-
lowing.

i.
Under the age of 18.
ii.
Has a physical or mental condition that re-
quires the personal care of an adult for at least
4 continuous weeks in the calendar quarter
services were performed.

b.
Your marital status is one of the following.
i.
You’re divorced and haven't remarried.
ii.
You’re a widow or widower.
iii.
You’re living with a spouse whose physical or
mental condition prevents them from caring for

your child for at least 4 continuous weeks in
the calendar quarter services were performed

 

If this is correct do I still need to fill a schedule H for income tax only and can I claim this as a childcare and dependent expense. Or will this invalidate the exception and I will have to collect nanny tax?