The road for chess development will never be smooth (true for all meaningful endeavor), so when your kids are losing several games in a row and stuck in trough, they need your love and encouragement. Sometimes they need borrow your confidence. They need this love and encouragement very often. Coaches are impossible to provide that.
Second, because kids only study with their coaches once or twice a week, on other days, you have to help motivate your kids to do homework and assignments. Many kids will not remember, especially when they are very young, so a gentle reminder will help. You must help your kids establish a good study habit.
Third, kids may not tell their coaches the truth of their study at home, either they can not explain well, or they only want to tell something their coaches like to hear. It's like what happen between kids and doctors. As parents, you are responsible to communicate with their coaches and provide them a real picture. You and the coaches have to work together to provide your kids the best help.
Fourth, you can always learn to play chess. Most coaches will not care if you sit along with your kids in private lessons. By playing chess yourself, you are setting up a great role model for your kids. Initially as an adult you will progress much faster than your kids, but they will catch up soon. Beating you will be the first milestone among their numerous achievements.