Like you said yourself, he probably just find lateral work hard to start with - my mare does! I actually allow her to slow down for giravolta, as well as other lateral exercises, as I think slow but correct is better than forwards and hopping. Personally I'd just settle for slow and steady for now... When you get correct work, even if it's slow, it will gradually strengthen him and he will start finding it easier and you can then ask for more forwards. I tend to do a bit of lateral work, then straighten and ask for nice forwards marching steps so that I don't get stuck in the "slow mode", then ask for bit more lateral etc.
When I had my lessons with Becky H, she also wanted our lateral work to be slow and steady.

Having said that, Nell has loads of issues and is a rehab case, so what she needs may be different from your horse... You'll just have to get that Becky clinic organised really soon, she will keep you right!
