This is allowable unless these dictates can be show to be based on unlawful discrimination, which you do not allege. You are most likely an at-will employee. Absent a contract, the employer can dictate hours, if they will provide vacation pay and when you may take vacation and any number of other conditions.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
Yes they can. Otherwise the employer could be left with all the employees taking vacation at the same time, or perhaps during the busiest time of the year. Unless you are the only employee who is being told when you can take these hours, and you believe this is because your employer is discriminating based on a legally protected reason, than your employer does have a right to approve when you take your vacation time.
This advice is general and based on what you mentioned in your question, not necessarily facts, and therefore you should not rely on it without scheduling a consult with an attorney so that he/she they can inquire further as to the details and review all pertinent information prior to you making any decisions.