I am a US citizen living in the UK with a British family and have looked into this extensively. Your father can go to see her if she is a US citizen. This is because the presidential proclamation ("travel ban") does not apply to immediate family members of UK citizens. A son is an immediate family member.

Please see US Embassy evidence FAQ 1.1 here, which confirms this:

https://uk.usembassy.gov/visas/u-s-visa-and-travel-faqs/

He should have evidence of her citizenship and his relationship to her. It may be unhelpful to mention things such as vaccination as they are not currently considered.