How often is D with Ex?
Per the above, 7pm is good. Say hi, small talk and goodnight.
My Ex does the same thing. Though she doesn't give an option, she outright says "Call me in the morning before school." Tough request for a 6yr old as it's pretty hectic in the mornings before school. Wake up, eat breakfast, get dressed, brush teeth, do hair and watch a few minutes of cartoons with me prior to the bus coming. Really no time to work in a phone call. Nor does D even think of calling her mom because she's distracted with other things. So distraction is the key.
I assume your D is in Kindergarten. Or regardless, your mornings are just as busy I'm sure. If your D is distracted with other things or being entertained, calling someone on the phone is not going to be of her interest.
OH - Residential parent of D5 after a long distance move by Ex. If your child(ren) aren't a priority, you will have no chance at gaining custody.