Presuming that these domestic flights are on a separate ticket from the UA website provides a useful calculator. Bear in mind that as there are two of you, you deal with each passenger separately. You do not have 3 bags, one of you has 2 and the other has 1.

If you are on a single ticket from the UK, the baggage allowance for the marketing carrier of the first segment will apply to all subsequent segments.

https://www.united.com/CMS/en-US/tra...edBaggage.aspx

I strongly urge you not to pay in advance. There is no savings and if there are changes in IRROPS, it will take forever to recover the fees.