Resident of the UAE here. My child and I have different surnames, and once I have been questioned coming into the country with him (“where is your husband??”).
There was some talk in the UAE papers last year about new requirements for travel with minors, but seemingly nothing official ever got released and it appeared that it was possibly specific to travellers arriving from India.
Immigration are unlikely to bat an eyelid if all travellers have the same surname, based on what I have been told by friends who travel in and out frequently. That said, always better safe than sorry, in my opinion, and you never know if you’ll get an immigration guy in a bad mood.
I always travel with my child’s birth certificate and a letter of no objection from my husband. Have also been questioned in the UK, but that’s beside the point here.

If trying to enter Canada by air as a solo adult with young child(ren), Canadian border control authorities will often ask about a letter. If transiting airside at YYZ or YVR or YUL, not as commonly. If trying to enter Canada by air, then almost always IME.

The variable approaches that go on with any given country’s authorities are far worse when the family doesn’t fit the racist and sexist (and maybe ageist) prejudices of the personnel encountered. And then letter or not, it’s best to go into the situation informed about what is actually legally required with regard to written permission forms before even traveling and being prepared (along with preparing the children as much as possible) to stand one’s ground while prepared, letter or not, notarized or not, by answering confidently and consistently.

I have witnessed enough “making up rules” and inconsistent, unfair encounters from passport control authorities when it comes to family travel, that, except for in countries where it’s legally required, I don’t hold much faith that a letter with a notary or not will make all that much difference. What makes a difference more is what the border control individual thinks about the family upon seeing them and the behavior of the people in the travel party and how they do or don’t fit into the personal expectations of the border control personnel encountered.

Would I suggest that the grandparents have a letter from the parents? Yes. I would also suggest having a smartphone that works abroad to make video calls to the parents and having the parents ready to answer at around the time the kids and grandparents get to the passport control checkpoint. Being in a position of confidence and well-informed about the actual legal requirements in advance of travel is the best pre-emptive defense to what goes on at airport passport control checkpoints.