Can an individual in a married couple hold custody of their children until a court date is set?

Not if she asks, but if she does not make an effort to see them, you can use that against her.

You appear to be saying two different things. You mention that you and your wife have agreed to share custody during the tendency of your divorce action, but then state that she does not keep the kids in her care and custody when it's her turn. The agreement is meaningless if your wife doesn't comply with it. This means that you are essentially the sole custodial parent during the tendency of the divorce action. Not because you are deliberately withholding the kids from your wife, but just the opposite: she is not taking responsibility for them. Thus, you are not keeping the children from her, she is staying away from them. You are not only not at fault, but are behaving honorably as a responsible parent, apparently the only responsible parent of the two. Keep a calendar that records all the time the children spend with you and with your wife. She will likely claim that you and she had an agreement to share custody, and then claim on the basis of that agreement alone that you and she did in fact share custody. You'll want to keep records that demonstrate otherwise. You will also want to make sure the neighbors (as many neighbors as possible) are aware of how often the children are with you overnight. Again, the reason for this is to debunk any claimed your wife might make to sharing custody voluntarily.

No. You can't make her be a good mom. But you also can't alienate the children from their mom. Continue to try to communicate with he about seeing the children. Keep a journal of her visits. Then present if to the judge. Mom will most likely get every other weekend and pay you child support.

It can hurt your case if you withhold contact. I never recommend that unless there is a threat to the safety of the child. With that being said, keep track of the days she misses until there is a more formal court order.