BD”E.
Amichai – there are no halochos of aveilus for a grandchild. The halocho is Kibud av v’em, that when a parent is sitting shiva, a child keeps certain halochos of aveilus until the first motzei shabbos (hot showers, music etc.). These halochos are regardless of whether the parent is sitting shiva for his/her own parent, or if the parent is sitting for another relative (spouse, sibling etc.)