Poor little girl. I don't say that as a criticism of you - I feel for you too. But I think you really need to not lose sight of the fact that this is a tiny child all in a mess and that's not her fault.
I would say don't be so quick to blame everything on her mother - who I do think sounds like a bad parent for dragging her daughter into her own difficulty dealing with her ex moving on.
You're very quick to say the child wants her dad in the night because her mum coslept until 2. Regardless of what you feel about co-sleeping yourself, note that it was til she was 2. Not now. So how is that because of co-sleeping? My 5yp still co-sleeps with me, it suits us. She doesn't with her dad (divorced). It's just about different rules and expectations.
I am a fan of co-sleeping (obviously!) so I personally think she should be in with you and dad whilst she's so vulnerable - but I know others would have a different view!
Anyway, that's just an example of how I think it doesn't help to blame her mother for everything - I think the cosleeping request is because she's insecure about her dad.
I also think it's possibly fair enough she's up for the holidays - it's his daughter! A working farm is not an easy place to keep a child entertained. Should she even be there? Why hasn't he put her in a holiday club? Is there someone to look after her? (who has the baby - you must be working opposite shifts to your partner?)
I really echo what others say about kids accepting two sets of rules. If she's rude, don't stand for it. Give her the food you eat, and expect her to eat it. Whilst at THR same time recognizing that baked beans are not the worst food in the world!
When she says her dad only loves her sometimes, he has to correct her and reassure her. "Daddy doesn't live with you all the time, but Daddy loves you all the time".
Love bomb her, whilst being firm with your house rules.