Does Mom's 100 days start over?

It sounds like your mother is being treated within the same "spell of illness."

Medicare pays for "inpatient hospital services, post-hospital extended care services, home health services, and hospice care . . . post-hospital extended care services for up to 100 days during any spell of illness..."
42 U.S. Code § 1395d(a)(2)(A) - Scope of benefits
https://www.law.cornell.edu/uscode/text/42/1395d

42 USC Section 1395x(a) defines the term “spell of illness” as a period of consecutive days—
(1) beginning with the first day (not included in a previous spell of illness) (A) on which such individual is furnished inpatient hospital services, inpatient critical access hospital services or extended care services, and (B) which occurs in a month for which he is entitled to benefits under part A, and
(2) ending with the close of the first period of 60 consecutive days thereafter on each of which he is neither an inpatient of a hospital or critical access hospital nor an inpatient of a facility described in section 1395i–3(a)(1) of this title or subsection (y)(1). 
https://www.law.cornell.edu/uscode/text/42/1395x

From Medicare.gov:
https://www.medicare.gov/coverage/skilled-nursing-facility-care.html
"If you stop getting skilled care in the SNF, or leave the SNF altogether, your SNF coverage may be affected depending on how long your break in SNF care lasts.

If your break in skilled care lasts more than 30 days, you need a new 3-day hospital stay to qualify for additional SNF care. The new hospital stay doesn’t need to be for the same condition that you were treated for during your previous stay.

If your break in skilled care lasts for at least 60 days in a row, this ends your current benefit period and renews your SNF benefits. This means that the maximum coverage available would be up to 100 days of SNF benefits."

Confirm with your health care providers whether your mother's care was within the same "spell of illness."

My understanding is that she must have not just been admitted to the hospital, but, must have had a stay of 3 days or more in the hospital for acute care

And, if she was at the hospital for 3 or more days, check to see if they "admitted" her under "observational status". Even though she was there for 3 or more days, if she was under observation, it will not count towards the required 3 day admit stay and thus the 100 days for a follow on rehab stay. Also, the rehab stay is only for 100 days if she continues to need SKILLED rehab or nursing and if she does not show improvement within that 100 days, then she could potentially be discharged or taken off the Part A portion of that Medicare benefit. Talk to a hospital ombudsman for information as it pertains to your Mom's situation.

The hundred days only starts over if she was admitted for a totally different condition. From what you stated, I can only assume she is back in the same place for the same condition, so no restart.

She went in originally for confusion and uti

Thanks

This information should be helpful! There's some fine lines in how Medicare pays for the care that's needed. Follow this link:
http://www.aarp.org/health/medicare-insurance/info-08-2010/ask_ms_medicare_question_86__.html hope this is helpful!

One must spend three nights in the hospital after having been admitted for the "Medicare clock" to be set to zero.

Each "spells of illness," as it's called qualifies the patient to start the 100 day cycle all over again, e.g. it must be a separate illness.

either the discharge planner at the hospital or the social worker at the nursing home is best suited to help you answer this question