Hi Paul,
Not a good situation and not one that will be remedied easily if there is someone who wishes total control.
The only thing you can do to establish any form of enforcible contact is to have court orders in place or in some states I think parenting plans are now acceptable.
Right now in her eye's she can control the situation, she has the power and she does not intend to let it go quietly, even though this is an abusive use of your daughter to serve her own purposes she will carry on doing this until it does not serve her or she is told by a person in authority that she has no right to abuse in this manner.
Like it or not in more cases than not we have to fight for the right to be a caring parent and to do this we have to jump through the expected legal hoops, the nearest thing to a short cut when someone refuses to discuss issues like a grown up is to follow the path of mediation rather through the court or a mediation centre. Remember mediation can work if both parties are willing to participate but if one party chooses to be non-receptive ( obstinant ) then it will not work.
The sooner the better, when application is in place then apply for intrim orders if you feel that contact is not enough, although you will most likely recieve less than your request it is a start.
Your daughter will need stability to best prepair her for her life ahead so even every second weekend and two nights every opossite week is so much better than contact at mums discression when she feels that you are deserving.
I can not express enough how this is a prominent weapon of Alienators, it is very controling of both yourself and your daughter and generates nothing possitive to your daughter and is subject to the whim of an unbalanced person, your girl will really appreciate any stability you can achieve, but remember not to play the game your daughter will need a place that is stable and will react badly if you dis her mum.
Sorry about that I just really hate P.A.S.
Try to look at long term solloutions not short term but keep the short term as your base this may turn into a bit of a haul and you will need to have contingesy plans in place for holiday perriods when you move where you access your daughter for contact, which will cover any moves that you may have to make.
I'm sorry I don't know any short cuts but if you want to talk about things and where you might start as well as what you may have to consider just pop another post on.
You do need to be very wise and not push your X to communicate with you and be careful not to send too many S.M.S.'s, letters, phone calls, E-mails or contact through third person. There are some very charectoristic traps and triggers set for you to fall into if you are unaware of them.
Best of luck with your decissions
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I never offer advice just options that might not have been seen.