It sounds as though you are correct in assuming that all the cousins are vying for attention from their grandparents. Although you don’t indicate how many cousins are in the group, you make it sound as though there are quite a few. Your daughter, as the youngest, probably doesn’t have the coping skills the older children have and tries to manage the best she can. Grandparents are a great gift to children, but your parents may be overextended with all the cousins and may not have the energy or patience to supervise them adequately when they are responsible for the whole bunch. In that case, the older ones are quite likely to take advantage of the younger and smaller ones, leading to outbursts. I would suggest that, any time your daughter is going to be with all the cousins, you try to be somewhere close by. If you sense an outburst building up, step in and try to avert it. If one happens, whisk your daughter out of the room until she calms down.
You say that you live with your parents, as does one cousin who has been raised by them. It is quite possible that, in addition to the difficulties of holding her own with a group of older children, she has some identity confusion. If the 6-year-old, who lives there and has been raised by the grandparents, considers them to be his parents, your daughter may feel that she has as much “right” as he does to attention and affection from her grandparents. Although in America we tend to glorify the extended family and look back with nostalgia to a time when it was more common, it is not an easy situation. Both you and your mother may unconsciously be trying to make certain that your daughter loves you the most. She will quickly learn how to play one of you against the other, which won’t be good for anyone. Stay alert.
Incidentally, your main allies are going to be the cousins. You will understand and excuse her behavior; they won’t. Before the kids get together, simply remind your daughter that if she bites or hits, her cousins won’t let her play with them. That should be helpful.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.