The situation is obviously this: A is B's child and asking permission for him- or herself and at least one other person.
In the first sentence, the subject is "we". When you use the first person as the subject, "go" implies motion away from the person being addressed. A is addressing B, so A wants to go to a place where B is not located. If A had used "come" in this sentence, it would have meant that B was already at the movies -- perhaps B worked at the cinema.
In the second sentence, the subject is "you". When you use the second person as the subject, "go" implies motion away from yourself. "Come" would mean either motion towards yourself, or that you wish to accompany the person you are talking to.
Look at these alternatives:
A: Can we come to visit you?
B: As long as John comes with you.
(A wants to visit B -> motion towards B, "come" in both cases)
A: Can we go to the park?
B: As long as John comes with us.
(Motion away from where A is -> "go" in the first sentence, but both B and A are going to the park -> "come" in the second sentence.)
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