Aunt Miriam is Grandpa Lou's cousin. Similar to how Angelica is Tommy's cousin.
Miriam refers to she and Lou having friends named Bill and Jill, similar to Tommy's friends Phil and Lil.
Aunt Miriam refers to incidents that happened when she and Grandpa Lou were children and they all have happened to Tommy in previous episodes. Such as Miriam leaving Lou's window open and causing him to be sick, Lou getting stuck in a hole in the garden and his friends Bill and Jill helping him out, and Miriam throwing Lou's ball over the fence into the neighbor's yard and them having to retrieve it. All of these things have happened in previous episodes to Tommy. Edit: Tommy never got his head stuck in a fence. Angelica did in a flashback in one episode; Chuckie got his head stuck in a tree stump in another, and Tommy was trapped on one side of a fence in the same episode Angelica threw his ball over it.
Aunt Miriam says Angelica is just like her, and doesn't realize she is very correct in her assumption. Since she refers to incidences that happened in her childhood with Lou, and Angelica has done those same things to Tommy. At one point Lou tells Miriam he was terrified of her when they were children and she always threatened to beat him to a pulp. Similarly Tommy is terrified of Angelica and she is always threatening Tommy and the other babies.