I don't think spaying will change her behaviour much, it never has with any of mine. The only changes were that they were prone to weight gain and their coats went mental. I think maybe your needs more mental stimulation and excercise. I know you say she's had training but maybe some agility classes might help give her something to think about and tire her too. More excercise would certainly help but if you don't have time for longer/extra walks you could try a doggy backpack.
http://www.doghaus.co...4KJpqoCFVEKtAodt0OGhQ . You might also want to look at how you react to her 'bad' behaviour, you might be unintentionally rewarding her and encouraging it. If she screeches and leaps about when you pick up the lead, put it down, turn your back and walk away. Ignore her until she's calmer then try again until she learns that only by being calm will she get the reward of walkies. It takes a lot of perseverance and patience and you need to be consistant but she sounds like a very intelligent dog and she will learn. Food suppliments might help but I don't think there is an instant fix, you need to put in the time but I'm sure she's worth it.