No, Leicester and Royal Holloway would be better than Open U.
Look at the Leagues Table (rankings) and see if higher ranked universities have online programs.
So, your parents have about 5K per year in college savings; do you know how much they can use from their income each month in addition to that ($500?? $300?) Add 5.5K in federal loans and you have your basic budget. Any scholarship you earn would increase that basic amount.
Because scholarships depend heavily on test scores, it may be well worth your time retaking the SAT and/or ACT.
For history, you want a university with strong preparation in the major areas and periods, a French department (typically required language for history), and if interested in archeology, strong classical language&civilization.
Does the small university offer those? What sort of university is it (public, private, religious…), their 25-75 entrance test scores, criteria for the honors college, top 5 majors?
(Can’t you indicate what it is? It’d really help in helping you make a determination. There’s a difference if it’s UNC Asheville and Geneva, for instance…)