I always taught mine to gait in hand using double long reins and a surcingle. Always start with a flat walk. A good flat walk is the base for a great running walk. Slow her down and get her back to basics. When she paces, shut her down and start back up immediatly. Gaiting in hand can be difficult because some horses tend to look for extra balance in the bit and bridle.
Teaching to stretch out for the park is pretty easy. Get her back legs square. Pull her wither towards you and tap with your toe at her fetlock area. If she doesn't move, pick the leg up and place it about 6" ahead of where it was. When she bares weight on it, give her a cookie and a pat. Do the same with both sides. It takes every day practice and dedication but eventually when you grab her withers or tap her elbow and say "park" she should climb into it. I like a horse in a park to be pushing up into it. Leaning on the forehand. To encourage that, once she is in her stance, hold the lead up high and a bit forward. She should lean but not move from her stance.