What is the name of the older cousin who often bullies the babies?

The older cousin who often bullies the babies is Angelica Pickles.

Angelica is Tommy and Dil Pickles’ three-year-old cousin and one of Rugrats’ central characters. She is spoiled, manipulative, materialistic, and frequently uses her age and ability to speak clearly to control the younger babies. Her bullying often involves threats, lies, demands, or deliberately misleading translations of adult conversations.

Angelica is not simply an unrelated neighborhood child: her father, Drew Pickles, is Stu Pickles’ older brother, making her Tommy and Dil’s first cousin. Her rivalry with Susie Carmichael is another recurring part of the series, since Susie often challenges Angelica and protects the babies.

A common mix-up is confusing Angelica with Kimi Finster, who is Chuckie’s stepsister and later adopted sister. Angelica’s character was created to give the series a child antagonist, although later stories also show that she can care about Tommy and the other babies.