As a father i have a similar issue with the children (daughter aged 11 and son aged 6) staying with me and when things don't go there way they then say they don't want to see me.
It upsets me that sometimes my ex does not help with regards to helping the children understand they have two homes.
ie the older daughter will complain that the toys she wants are at ex's home. Now these are toys i've bought and then end up at other home. When children bring toys to mine that ex has bought I will always endeavour to ensure that they return to other home.
The key thing to work out is what are genuine issues (ie shouting/stressed dad) and what are consequences of having "two homes".
A 6 year old will find it very difficult to articulate this and you do not want to have a conversation along the lines of "what don't you like at daddys" as that may reinforce a negative impresssion.
What can help is find out what your daughter has enjoyed about being at daddys.
If you are on speaking terms with your ex you could see if he could start some traditions that your daughter does at his home
ie my daughter gets to have a hot chocolate once son is in bed .
I bought a blender and my son and I make smoothies with "weird combinations" of fruit and juice.
My daughter enjoys playing candy crush so we play the same levels side by side and see who gets best score.
My son and daughter both play UNO with me.
Now even with those kind of things i still get when things don't go their way (ie when they have to eat at table or have a hair wash they say "i want to stay at mummys instead of seeing you" and it can hurt when they say that. )
Do you have a mutual friend that can maybe help/mediate.
It can be very difficult to have someone else (ie ex) tell you that you need to step up parenting techniques. But you can help by finding out things he does do well (be it nice day out, playing a game, dvd night) and letting ex know your daughter really enjoyed like doing x, y and Z.
Its much better to hear about positive things than negatives (and then attempt to slip the odd negative in with regards a positive spin. ie maybe your daughter complains about the food at your ex's. You could say "daughter is saying she's not enjoying the food as much as she used do you know that shes gone off a,b and c but really likes d, e and f)
The fact that you are asking for advice suggests your heart is in right place and hopefully the support you get will help. i