My horse is like this, it's horrible isn't it. We've had to camp at the showgrounds overnight before because we just couldn't get her on.
She's also not scared, just really stubborn. I stay calm and everything but she remains as calm as me and just falls asleep half way on but refuses to continue, then she swings her quarters out and makes it impossible for herself to get on.
When she swings her quartersnow I just belt her with the whip to bring her quarters back around, ask her on again and she goes striaght on all the way in, because she knows I'm not going to put up with her crap any more.
At my last comp straight after my ride once she was hosed down, I packed the car and loaded her straight up so she didn't have time to relax and get comfortable, and she walked straight in.
Do heaps of practise at home, even if she goes on perfectly, do it anyway..take her for a short drive around the block then back home, unload her, then load her up again. Just keep practising, I'm sure she'll get it eventually