There are two approaches on how this parenting conundrum is handled. One viewpoint is that if you have a joint parenting plan or a plan that is approximately an equal split with the other parent, what you do on your parenting time is your business (generally speaking) and what the other parent does is his or her business. Because you both get equal shared time, it is up to each of you how you would like to spend it with your children.
On the other hand, if you do not get as much time with your child as you would like, you may successfully be able to argue that you should have the right of first refusal to care for the child during the other parent’s time if they find themselves in a position of needing a babysitter or having an alternate family member care for the child while they are unavailable. It is generally accepted that it is better for a child to be in the care of a parent rather than other third parties, whether they are family or not.