There are many people in the United States caring both for children and aging parents. They are called the Sandwich Generation. To make this even more challenging, 65% of couples are duel income families with both spouses working. So, this can become an incredible juggling act with demands on time coming from both directions. The problem is there is only so much time in the day. The only way to succeed is planning ahead and great organizational skills.
This means taking control of events and not allowing events to control life. To do this, people have to see the train coming before it runs them over. So specific to aging parents making sure that where they live is safe and secure and outfitted to prevent falls. So grab bars in the showers and baths. Getting rid of throw rugs that often cause tripping and falls. Making sure that their shoes are sensible with the right no slip soles. Stocking up on foods in the freezer to diminish shopping needs. Scheduling doctors appointments at times that work for all concerned.
Specific to dealing with the kids. They have to do their fair share of work at home. Even younger kids can do house and yard work. School projects must be planned weeks in advance, if possible. After school sports requires coordination with other parents to share in rides. Convenience foods are a must because spending hours cooking meals is probably not possible.
The Sandwich Generation has reasons to be exhausted. Dealing with multiple generations can be a 7/24 responsibility. Even so, people taking care of both aging parents and kids must find time for themselves. Book time in the calendar that is sacred and don't let anybody take it from you. Set limits so the people you are caring for understand the times when you are off the clock. And, learn to just say NO.