I think you must work, If you can or you must PAY a programmer, in order to:
have one db, so one users table and maybe one table for common tables, maybe with the use of views (one table of users superset, and two subset views for blog and existing table (have two sites)
the other to choose one of the two admin page, and join the two admin pages, but the upper part is going to retrieve the info from the existig site and the lower from blog, so it is going to be a web page that is going to retrieve data from two different databases (if you do not have one db, with two sites))
It whould be wise to migrate the old site to blog and build the missing pages of the old site. In that case you are going to have one admin page a little modified (one site)
Usually all are in one site, except the case there are payment of software issues.