When you ask a horse to move off your leg, you aren't "pushing" him over, but using an aid that he has been trained to respond to. You can push your leg against a green horse until you're blue in the face, but if he hasn't been taught to move away from the leg pressure, he's just as likely to lean into it than move away. It's much like moving forward off the leg. If the horse isn't trained to do it, then he has no clue what you mean. However, even if he does understand it, he may stop when presented with something that he resists moving toward (e.g., refusing a jump).
So, there may be two factors to consider with your share horse. First, how well does she understand and obey the concept of moving off the leg in normal circumstances. Can she do a turn on the forehand? Leg yield in the school? Does she respond to a light touch, or do you feel like you're pushing her over? If the latter, you may need to do some simple, repetitive schooling to teach her to respond to lighter cues.
If she's sensitive and responsive to lateral aids in the school, then your issue is dealing with puddles in particular (and perhaps obedience or trust, in general). The next time she leans into your leg to get around a puddle, stop him, back him or circle him the other way, turn her to the puddle and send him back through it. Be very persistent and eventually, she should learn that (1) yes, you really do mean for him to go through it and (2) it's easier to just respond to your request to go through the first time since eventually she's going that way in either case. Part of the key is being more patient and persistent then she is.