You should definately talk to her. Say what you've said here, but try to remain as calm as possible. Ask her what she's really worried about. Make it clear that if you ever hang out with this kid, she will not be a topic of discussion and you won't force them to hang out. Make sure she knows that you'll be able to balance your time and attention on both of them separately. Lastly, you may want to gently hint that her demans are and controlling. Make it clear that you don't appreciate either and that if she's really your friend and trusts you (as she should) she should not be worrying about this.
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"Ignorant people see life as either existence or non-existence,
but wise men see it beyond both existence and non-existence
to something that transcends them both; this is an observation
of the Middle Way." -Seneca, Roman philosopher