(As an aside, I challenge anyone to justify the unsupervised provision of a 4G, Internet-enabled iPhone to a 7 year old. It is clear evidence that the RP in this case is acting provocatively against her ex, rather than in the best interests of the DC).
on the one hand, I agree but on the other, my 7 year old has a tablet and uses it (in the same room as me) to access the internet etc. He takes it to dad's house regularly - not because I am 'acting provocatively against my ex' but because he likes it and wants to use it there. I know my ex has far less tolerance than me towards the children sitting on tablets or the laptop or watching TV and he takes them out walking very regularly to avoid it. But I don't think it's for me to tell the children what they can and can't take between houses as it's their stuff and they have a right to have it with them. The children complain dad doesn't let them use their tables much as a result but that's up to dad, not me. I certainly wouldn't get involved or tell my ex he was 'wrong'. And even if I did, he wouldn't listen to me anyway!
I do get tired of the assumption that the PWC is deliberately trying to cause problems for the NRP everytime they make a decision that is contrary to what the NRP believes is best for the children. We've split it, for heaven's sake, we will parent differently and we will disagree on what is right and what is wrong. But I can no more influence what goes on in my ex's home than he can in mine as long as I let his crap go over my head and say 'yes, dear' and then shut the door and do whatever it is I want!
I think where contact has been problematic (no matter who's fault that might be), it is not unreasonable to allow a child the means to be able to contact their other parent at will. If mum provides the means, she's as sure as she can be that her child can contact her if she wants to. If she doesn't provide the means, she will be concerned that dad might play games and mess about and she'll be the one having to pick up the pieces of a distressed 7 year old who says she doesn't want to see dad again because she wasn't allowed to make that phone call.
I agree with frog that you have to find the middle ground and see it from both mum's and the child's perspective. That doesn't mean that you have no control over the phone in your home - far from it - but rather than focus on that, focus on being a loving, welcoming family environment with nice things to do/see/eat and see how things pan out. It doesn't have to be a fight.