IIRC (And my college classes were 2 decades ago, so could be quite mistaken, and I can't find the textbook) The Dominican Republic did want to be anexed, but the idea of adding that many negroes to the USA was the deal breaker.
Correct, iIn OTL the original effort was in tandem with negotiations to purchase Danish Vigins Islands, by SECOS Seward. Idea was control/defense of the sea lanes to the Panama Isthmus.
Started under Lincoln, treaty were signed with the Danish for St Thomas and St John (for $7.5 mil, the Danish motive for selling) in 1867. The Dominican Republic's motive was protection from Haiti (having seen the French intervention in Mexico), they offered bases, with outright sale or lease, or a treaty creating a "special" US protectorate status. All, both the Danish deal and the DR came to nothing because of President Johnson's problems with Congress. Treaty killed, and Seward dropped the DR idea.
The DR came back with an offer (this gets wild) to "
declare themselves annexed and work out the details later..." which Congress rejected.
Issue lived on because the Navy wanted a base in the Caribbean eventully a treaty fro annexation was signed between the USA and DR, but once again the Senate defeated it.
Appears the main issue was Republican infighting between the old school Norteasterns and Grant/ Western republicans, but the issues of the adding that many "black freedman," as well Catholics, and a general distrust of "southern" expanion played a part (also what killed efforts to buy Cuba and Jamica at the time from ever getting pass the discussion stages).
Two triva notes,
(1) one of the loudest voices for annexing the DR and
Haiti was Frederick Douglass, even served on a special commission regarding the annexation and lobbied Congress.
(2) Apparrently almost all the Central Amercian nations during the post Civil War period at least dicussed the idea of requesting annexation by the USA.