I think that reaction of your DSD is a bit unusual tbh - if you've been with him 5 years then presumably he split with her mum when she was no more than 4, so it should be normal for her. Or did he only move away from the home town much more recently? Is that the problem?
Is she happy at home? Well worth seeing if her mum have any insight into why she finds it so hard. Is it that she's already upset about something else so misses her dad, so phones him - but doesn't think about calling him at times when she's happy?
Does she have her own computer or tablet? if not, and you would/could afford to get her one, if she has Skype on that it might make Dad seem much more on hand than if she has to arrange a time to call him.
My DD is 9 - not sure she'd manage much of a conversation by email, isn't great on the phone, but she loves instant messaging on skpye, is begging for a mobile phone so that she can start texting, and does chat away to friends (or occasionally her dad) on Skype too.
My partner of five years has a nine year old daughter who we both love very much. She lives many miles away and she comes up for all of her school holidays apart from Christmas when my partner goes down to where she lives so she can spend Christmas with both her mam and dad. I get on very well with my stepdaughters mam, we have become friends and she came on holiday for a few days with us last year and me and my children (I have two teenage sons from a previous marriage) are going to stay with my stepdaughter and family for Christmas this year. My partner pays £50 per week maintenance whether N (my stepdaugher) is up on holiday with us or not. We cover all the train fares and other expenses, we would do more, but I am at university and my partner does not have a well paid job. The thing is, my partner feels guilty as he is not living on the doorstep of his daughter - he suffered a nervous breakdown after being a victim of armed robbery and moved back to his hometown to recover; its an ongoing process - and N finds it hard to talk to him on the telephone as it upsets her. This really distresses my partner as he thinks he is to blame for her feeling like this, therefore he is not a good father and she will reject him in future years as he 'was not there for her'. I have tried to reassure him that he is doing all he can, he genuinely cannot do more, and I wish my children's father was involved (he has not seen my sons for two years, but thats another story!) N really enjoys coming up for her holidays and refers to our home as her second home, but I was wondering if there was anything else we could do, or if anyone could offer advice on this? Has anyone been in, or are in this situation too? How is it working for you? I just want my partner to realise that he is an amazing father, and that N will eventually realise that although her daddy lives many miles away, she knows he is always there for her.