@jimbob1980, how is your son doing in terms of his development? Is he getting the support he needs or is it that your ex-partner simply copes better with him? What were the reasons behind her handing your daughter over to you?
You say your daughter stated her Mum was crying and then you go on to say your ex-partner told your daughter if she wants to move back in with her, then your daughter should speak to you. Do you know what the conversation between your daughter and her mum was?
What is your ex-partner's current living situation? You say this has developed over the last 4 months...
I have a 7 year old daughter myself and while as parents we want to always do what is best for them, I feel at this age in order to thrive, your daughter really needs stability, continuity and security, all of which it seems she is getting with you. The upheaval of moving her back in with her mum should ONLY take place if her mum can offer her the same environment and continue to nurture your daughter's development.
I get the whole 'speak to your child as an adult' but your daughter is only 7 and not emotionally equipped to tackle all of the smaller very complex issues that are encompassed within the wider issue, which in your daughters mind is that her mum is sad. Perhaps your daughter believes that moving back in with her mum will make her mum happy?
I would take advice from your daughters school regarding her development, perhaps seek counsel from a trusted GP who would be able to sign post you to services that may be relevant in helping you to decide what is best for your daughter and helping your daughter to understand why you are making the decision that you are.
Ultimately, please trust your instinct as her parent, if you know she is better off with you then you have your answer.
Also, please think about the situation with your son and how he is being impacted by his upbringing and the fact that he and his sister are growing up in seemingly different environments, apart. This will have adverse effects on their relationship as they grow into adults.
Best wishes.