I would like to translate the term "always loved" - referring to 2 parents. Would it be acceptable to translate this as semper carissimi rather than semper amati?
Yes, Lewis and Short supports this use.
[most, or very] dear, precious, valued, esteemed, beloved:
(Show lexicon entry in Lewis & Short Elem. Lewis) (search) It quotes Vergil, Lucretius and Cicero describing mater,pater; genitor, genetrix; and parentes as carissima, carissimus, and, for both parents together carissimi.