It depends on your expectations of clients children who are sick. If your policy is such that a sick child is expected to stay home and be excluded from day care to limit the exposure of other children and yourself, then that will be hard to enforce if you risk client's children when yours are ill.
If you are able to keep your children and the day care children entirely separate, using separate facilities and being supervised by your partner, then I see no reason for you to close. If however your children are young, will be mixing with the day care children and/or supervised by you, then I think it's unrealistic to expect clients to keep sick children home.
There's no right or wrong answer - this is going to come down to your own rules and policies but you have to be seen to follow the same requirements yourself or you'll lose credibility.
Since it seems you are intended to have sick days for yourself in the contract, and potentially vacation too, why not just label them personal days? I have 10 personal days a year. That gives my client limit to how many days they will need to find an alternative/back-up carer. Then, if I am sick, if I have an appointment I can't schedule outside business hours, or if I am taking some leave, it comes out of that 10 day entitlement I don't really have to worry or justify the reasons for it.