The phrase "proud grandma" means a grandmother who feels very happy and satisfied with accomplishments or achievements of her grandchildren. Full definition
Ruth Caro, nee Epstein, age 83, beloved wife of the late Seymour Caro; loving mother of Robert (Sherry) Caro and Marilyn (Steve) Jaffe; proud grandma of Michael, David, Rachel, Alexis and Christopher. (articles.chicagotribune.com)
Expect lots of baby photos and posts because like all of the other grandkids, this proud grandma will be the caretaker in chief while the proud parents work (shabbychicboho.com)