Really? Really? To leave home for a year and a half? To go without security, someone cooking and cleaning for them, without credit on their mobiles? For what? A laugh?
If the OP had said that her daughter had come back after a week mumbling about wnating her iPod back and some fish and chips, I would be leaning heavily on the 'teen ishoos' side of things, and I would, indeed, think that perhaps she had said it due to tensions elsewhere or out of spite.
But that doesn't appear to be the case. The daughter, from what we know, appears to be sticking to her guns, ie. removing herslef from the family home and sticking to her story.
I'll concede that I have projected my own family situation all over this, and for that OP I will apologise, but as I am sure you can appreciate, this is an emotive subject and will raise all sort of issues for you and others. I hope though, that my crazy strong reaction has made you consider your daughter's possible point of view.
I ahve to say thought that I think the 'odds' of OP's other half being innocent are, imo, bleak, based on the information given.
And I have never, ever, not while a child, teen, or an adult, had experience of any child, teen, or adult 'crying wolf' over abuse. I have known many children, teens and adults displaying signs of abuse struggling to come to terms with it, many simply having run away from home as soon as they could.
I am accused by my own family of being delusional, making it up and all that and I can assure you none of that applies in my case, but it is what abusive families do and say. This 'oh they make it up all the time' thing is a myth and one that needs challenging.