Depends on what she pulled the money from.  See this chart.  https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-tax-on-early-distri...

she pulled it from her NJ division of pensions. 

Only IRA's qualify for the higher education expenses as shown in that chart.  But she could use it for the medical.

She’s going to get hammered. But, I’ve had a few of these over the years that that we were able to roll into an IRA after the 60 days.

If she took the money out and spent it there’s not any recourse. But if a mistake was made and the funds haven’t been spent check out rev-proc 16-47… (there may be more current revisions). It provides for the self certification of a late rollover. The reasons are pretty broad.

 Last year, a client who was told her 401k from a previous company was closing and had to be taken out. The CSR explained nothing and 80k was transferred to her savings account. 6 mos later,  at tax time she got the good news… her bank accepted the certification, rolled it to an IRA and I was able to document the return. So far, so good….

https://www.irs.gov/pub/irs-drop/rp-16-47.pdf

Can she use it towards medical lodging like hotels at the $50 per night per person? 

Yes. You will want to refer to code sections 72(t)(2)(B) https://www.law.cornell.edu/uscode/text/26/72  and code section 213 https://www.law.cornell.edu/uscode/text/26/213