You need to read ancient Spanish documents and the information about Elisabet as fully legit Spanish form of Elizabeth in Diccionario de nombres propios
by Roberto Faure. Isabel is 100% Spanish, ok, but Elisabet is also 100% legit in Spanish.
A thing is the personal vision about a name, another the etymological/historical/legitimal facts about this name.
The spelling Isabella is only an Italian form, never Spanish. In Argentina, the Italian first names are very popular, but they are yet Italian names; used by Spanish speaking people, yes, but purelly Italian names.