(Not a teacher)
Either is correct here. 'In' is perhaps more correct, but if you said 'she skates at the park' no one would assume you mean outside the park.
If you say 'I will meet you __ the park' it is better to be more specific. 'I will meet you in the park' means just that - 'inside the park'. 'I will meet you at the park' means more 'at the entrance to the park'.