JJBFLY
I'm a former divorce lawyer undergoing a divorce with child contact issues, and I am a loco Captain, so I completely understand your difficulties.
However, like Back to Boeing, I've managed to keep things amicable with my ex and therefore my personal experience won't help much.
The sad fact is that where things have reached the court phase, you are fighting a rearguard action.
However my children do have the automatic right to see me if they so wished
is not entirely accurate. The presumption is that
it is in the childrens' best interests to have contact with the absent parent. Luckily my ex wholehearedly agrees. But it's not a 'right' as far as I recall.
Conversely, where the parent with residence is making contact difficult, your best bet is to take what you can get and hope that over time you can increase trust and flexibility with your ex. Once the children are old enough to voice their desires, the pendulum will start to swing back your way. Children have a habit of rebelling at certain ages. The absent parent then becomes an attractive refuge.
Good luck. I feel for you.