Why will she not be making weekly contributions to a pension if she goes self-employed? I assume it is the state pension you are speaking of.
If she is self employed she will be expected to pay towards her state pension. I suggest you look at this link www.gov.uk/government/publications/your-new-state-pension-explained/your-state-pension-explained Within this document several sections refer directly to self-employed people.
She can also make contributions to a personal pension as well, although contributions to the state pension scheme should take priority.
If she has rheumatoid arthritis, and is finding work the struggle you describe and she thinks she can make an adequate income going self-employed then I think that is a very sensible idea.
Bear in mind that if her income as a self employed person is below £12,750 a year. She will automatically be credited with state pension contributions. I quote from the above document
If you’re self-employed, your Class 2 National Insurance contributions are treated as paid if you have profits from £6845 to £12570 in the 2025 to 2026 tax year. You pay Class 4 National Insurance contributions when your profits are above £12,570 in the 2025 to 2026 tax year.
In your case I would be giving my daughter every encouragemnet to go self employed, but help her to set up all the paperwork she needs to satisfy the Inland Revenue.
As it is clear that you can afford it, why not pay a tax accountant to help her set up her accounting ssystem and explain to her what she needs to do and when to keep her tax situation in order?