Assume babies are born at hospital are independent events

This means there is no sequential ordering, no dependence on the outcome of prior steps. They are equivalent to simultaneous.

if the first two children born are girls

This question has been framed as if it refers to a sequence where there is a dependence on prior outcomes. By your own definition they are independent and thus not dependent, but the follow up question seems to conjecture there's a dependency.

Let's adjust that just a little, to merely identifying the individual births

How many possible outcomes are there to flipping three coins? 2^3=8.

How many of those eight possible outcomes are you counting as a success?

A AND B AND (NOT C)
For the sake of contrast, drawing cards from a deck is a sequence that depends on the outcome of prior steps. If I draw Seven of Spades, then the next draw will not be Seven of Spades.