I think it's not silly to ask for your parents to let you handle matters on your own. You already are an adult and about to be a mother, afterall.
It's pretty normal that parents tend to be very protective of their child. Your parents are just probably either really worried or really excited about the baby. :) I bet it's the latter. I remember my in-laws eager to spend time with me and the first baby in my tummy a few months before I gave birth.
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