Horse going sideways - fixing the problem - part 2

One of the ground exercises that I do with Lil is making her do a couple of circles around me, and going over a little cross rail while she's out on the circle.  Now I am very strict with going over the cross rail - there is to be no running out, no shying, no stopping.  Just a nice clean pop.  I don't mind (at this stage), whether she goes over it on the left rein or right rein, but she must go over it.

Has it all been going smoothly?  No, of course not.  We've had times when she's hesitated before jumping the rail, when she's tried to run out, and when she's tried to avoid it by changing direction.

Today I have set up the cross rails so that there are plenty of them - around our lunging area.  I stand in the middle and ask Lil to go out on the circle.  I don't ask her to do the cross rails, and there is plenty of space for her to circle.

I notice that she glances at the cross rail.  Well, if she's that keen to do them, then why not?  I build enough slack in the lungeing rein.  Lil feels the slack, lines up the double and jumps the two cross rails perfectly.  On the surface I remain calm, although perhaps my jaw has dropped, but deep down inside I let out a huge "YES!".

So how is this related to "horse going sideways"?  Well, she used to get very nervous when I used to ask her to jump those cross rails.  Yet now she has learnt to do it, and does it by choice.  Which means, I should  be able to use the same methods to teach her to go forwards, and not sideways.