The correct English translation of "ты ещё нас всех переживёшь" is "you're still going to outlive us all", which is obviously intended to mean "you still have much potential, much life force, so much that it will suffice for you to live longer than all of us". However, ещё is a polysemantic word, apart from its adverbial meanings "still, yet, already, additionally" one of its meanings is "so far" (пока что, meaning 4) and another (meaning 11) is to show reproach, irony, like in "Ты ещё скажи, что собаки летать умеют!" Also, it can express concern:
Надо позвонить, а то ещё решат, что мы погибли.
Let me call in, lest they think we're dead.
А то еще на вопросы отвечать придется…
Don't want to answer any questions…
The last three meanings and especially the last one can interfere with the correct understanding of ещё in your phrase, instead of wishing long life the phrase can be understood as the speaker's concern that grandma can outlive them. If the grandma is paranoid enough, she can understand the phrase as "so far, you can outlive us all[, but we'll take measures needed to prevent that]" or as "[don't you try to] outlive us all".
To resolve the ambiguity and make the phrase really inspiring and cheerful, the word ещё can be just omitted, or moved to another clause or sentence, for example:
Ты ещё много всего успеешь, да ты и нас всех переживёшь, у тебя ещё много хорошего впереди!