Make sure the changes are such that you, your subordinates and your company are better off because of them. It's important for both you and your new assistant manager to understand that it's natural for her peers to have negative feelings about her good fortune in being promoted. Some may feel they should have been chosen over her. Some may feel the things they've done and said about her in the past will be held against them since she's now in a position of power. Remember, these feelings are to be expected.
Rumors are natural.
Saying negative things about why you chose her for the position is normal. However, they won't be long-term problems unless you or the promoted employee feed them. One positive thing you can do is to advise her on ways to be most effective during the first few months in her new position. If both of you follow these suggestions, it should lead to minimal negative reactions and maximum positive ones. First, remember your mission and your assistant manager's mission is to create successful employees.