Yes, I'd like to find a solution that works without resorting to courts too, but it needs to include all children not just 2.
One of my reasons my ex has said I can't have them for longer is exactly what you said - because she only then has them for one weekend. While I can understand this, it is difficult to swallow because I cannot see them during the week otherwise there would be no problem. She sees them every day, and while indeed weekdays are different from weekends, I know I would give anything to have that same opportunity.
I feel I am somewhat paying the price for her moving further away, and there has to be some level of compromise from her part.
Listen to Sera, she is talking sense - as are the rest who have replied to date - and you really don't want to go to the Courts, I promise you.
Your real difficulty lies in the question "what rights do I have?" Unfortunately, as far as the Children act is concerned, none. I'm sorry, but there it is. Contact is a right of the child, not of the parent.
Your daughter has strong feelings, she is nearly an adult, and the Court would without question listen to all of the children but especially her because of her age.
We borrow our children. We have the care of them for a time. The test of our love is whether we are prepared to give them their freedom. What you wish to hold on to, let go of. What you hold too close, you stifle. The most important aspect of contact is not duration, nor frequency, but the quality of the time you spend together. Mum sounds as if she has a point. It ought to be possible to build agreement for all, try mediation - it does work.