The term 'Dutch' cousin or 'Dutch' uncle usually refer to someone that is treated as family, but has no actual relation to you. Typically a Dutch cousin would be the kids of some of your parent's best friends or perhaps step children of real aunts and uncles.
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Your mother's first cousin is YOUR first cousin, once removed. The child of your mother's first cousin is YOUR second cousin.
The child of your first cousin, once removed, is your first cousin, twice removed, if your first cousin once removed is the child of your first cousin. If your first cousin once removed in the first cousin of one of your parents, the child is your second cousin.
Your parent's first cousin is your first cousin, once removed. Your parent's first cousin, once removed is your first cousin, twice removed. Your parent's second cousin is your second cousin, once removed. Your parent's second cousin, once removed is your second cousin, twice removed.
If a cousin has a baby, the baby is a cousin one further time removed to all other cousins of the parent. If the parent has a second cousin, the baby is a second cousin, once removed, to that person. If the parent has a first cousin, once removed, the baby is a first cousin, twice removed, to that person.
The aunt of your first cousin's child is your first cousin's sister, who is also your first cousin.