I don’t think Gold would send Belle to the convent. He blames the Blue fairy for him losing Baelfire so for him to then put the one other person he loves into her care just wouldn’t make any sense. Also, Belle is probably safer off with him where he can keep an eye on her. He lost her once already when he sent her away from him, so I don’t think he would risk making the same mistake twice.
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All magic comes with a price!
Keeper of Felix