1. Frequent phone calls to the children. Many parents want to be able to call the children, or worse, want the children to call the parent, every evening or at other times and frequencies. Almost always, that leads to arguments. The parent who has the children doesn't want to interrupt their activities. Sometimes the kids are out somewhere, but the other parent doesn't believe it, or sometimes the parent in possession intentionally makes it impossible for the other parent to talk with the kids. Often the kids don't want to stop playing, watching videos, texting or talking with their friends, even doing homework, in order to talk with the other parent. In some situations, the parent with the kids sets up something that conflicts with the scheduled call time so the kids are available or the kids don't want to stop what they're doing.
For some parents insisting on the calls, it's a control scheme. They want to lock down the other parent and prevent them from being able to plan activities at certain times and they like to threaten court action against the parent in possession
There are so many different ways that problems come up, it's generally better to not require such calls. Another alternative, depending on the age of the children, is for the non-possessory parent to provide cell phones to the children. Then, the kids can call or text the parent or the parent can call or text the children anytime.
2. Right of first refusal. While it sounds like nice idea for the non-possessory parent to have the right to take care of the children if the other parent won't be around to care for them for a while, the devil is in the details. How much time is needed to trigger the provision: 2 or 3 hours, 6 hours, overnight? What are the notice provisions? What if the kids just want to spend the night with their friends or other relatives? Why shouldn't grandparents get some time with the kids?
While this sounds like a parent wanting to spend more time with their kids, it often is a control mechanism as well. It's a way to isolate children from one side of their family if they don't get to spend the night with relatives. There is frequent conflict over how the right of first refusal applies in a given situation. A big part of that is threatened litigation and punishment.
Given the fighting and stress over this issue, you should think twice before incorporating it in a court order.
3. Weeknights in the summer. In the Texas standard possession order, the non-possessory parent usually gets the children every Thursday night during the school year. It's limited to the school year because the schedule changes so much in the summer when each parent can have the children for 2 to 3 to 4 weeks at a time. Adding weeknights in the summer ends up potentially shorting the time of the possessory parent. I have seen a schedule where the schedule was manipulated and planned so carefully that the possessory parent ended up with only about 4 days total in June and July. That's not right for the parent or the children.
Extra weeknights are not needed for the summer. The standard possession schedule gives plenty of time for each parent and it doesn't encourage fighting or greed.
These are all three ideas that sometimes can be good for both parents and children. However, I recommend against using them because most often they lead to conflict that could be avoided.