You said: "So, if you have a strong relationship with your child, and SHE is saying she doesn't want to stay over or come, please do not immediately jump to PAS. She may just be expressing her needs and it's our job as parents to respect our childs needs."
One of a child's strongest needs at that age is to bond with and align herself with the person who is responsible for her existance - no matter how messed up that individual and their actions or desires may be. That means that if your daughter in any way interprets her spending time with her father as something you don't like or would hurt you - she will resist it, regardless of how much she may want to.
At her age, she is unable to put into words what her feelings mean. If she observes that you are anxious (or, say how much you will miss her, for example) when it's time for her to spend time with her Dad, she will feel anxious too - and describe her feelings the way you describe your own. In her mind, you and she are not seperate people yet. No four year old can articulate feeling that "we haven't spent enough time together". Maybe this are your own feelings that you're projecting onto your daughter.
Your job as a parent is to make sure that your children grow up happy, well adjusted people who are able to take care of themselves and their own offspring - not cater to their emotional whims. There are lots of things kids don't want to do that are important and best for them - eating their veggies, going to bed on time, going to school, going to the doctor, wearing a jacket when it's cold out... the list is endless.
You mention that you always make sure she really doesn't want to go - this type of interrogation is most certainly coaching. I agree with your ex. If your ex was on this board I would encourage him to use the courts to protect his right to parent his child. Hopefully you won't give him any more reason to.