As a general rule, you will NOT be allowed enter the US coming from the UK (or most of Europe).
The full details of the rules are available here, but realistically the only way that you would be allowed enter on the grounds that your father is a resident of the US (presuming he is a "permanent resident". ie, a green card holder) is if you were under 21 years of age and unmarried.
The only other option would be for you to have not been physically present in the UK (or the Schengen region or several other countries, listed here) within the 14 days prior to entering the US.
Vaccination status currently does not have any impact on these rules, and even if it did, being anything other that fully vaccinated (in your case, 2 weeks after your 2nd shot) would almost certainly count for nothing anyway.