Everyone faces hardships in life. One of your team members may be dealing with a child suffering from cancer. They may be struggling to take care of a parent with dementia. They may be going through a divorce. Whatever it is, it will surely affect their work.
When a member of your team is suffering, ask yourself how you would want to be treated if you were in their shoes. Ask the rest of your team how they would want to be treated. Because at the end of the day, you are still a team. And teams stick together.
So, the parent with a sick child may need time off. Can others help cover the workload? Will you pay them after they have used up their vacation time? Decide what you can tolerate and be upfront with them. You will not regret going above your obligation as the team leader.