Hi there,
As you correctly assumed, you may not be able to obtain supplementary health insurance coverage for your daughter if she has a preexisting health condition (though you can still apply). However, the added value of Swiss supplementary health insurance policies for your situation is marginal.
1. Specialists
Swiss compulsory health insurance provides unlimited coverage for the cost of treatment by specialists in Switzerland. If you opt for a managed care policy in order to save on premiums, you will have to get a referral from your general practitioner, HMO center or telemedicine service (depending on the managed care model used) before you can begin to obtain treatment from a specialist. The standard model allows you to visit specialists directly without referrals.
Treatment outside of Switzerland is not covered by compulsory health insurance except in the event of medical emergencies while traveling abroad or regular treatment when equivalent treatment is not available in Switzerland. Medical emergencies abroad are covered up to a limit equal to twice the cost of equivalent treatment at a hospital in Switzerland. When equivalent treatment is not available in Switzerland, a doctor in Switzerland must present your case to your health insurance provider, which will then decide whether or not treatment abroad is justified.
Swiss supplementary health insurance policies typically extend the travel medical emergency insurance which you receive from compulsory insurance (to 1 million francs, for example), but the coverage provided by compulsory health insurance is sufficient for travel to most countries. Supplementary policies do not generally provide extended coverage for regular treatment outside of Switzerland.
2. Hospitals
Compulsory health insurance provides unlimited coverage for treatment and stays in the general ward of a hospital in the canton in which you reside. Stays in the general wards of hospitals outside of your canton of residence are fully covered in the case of emergencies and when necessary facilities are not provided by a hospital in your canton of residence. In all other cases, when you choose to receive treatment at a hospital outside of your canton of residence, coverage is capped at a limit set by your canton of residence.
Supplementary hospital insurance extends the coverage provided by compulsory health insurance by adding coverage for semi-private (2 beds) or private hospital wards. It is worth noting, however, that the general wards of many Swiss hospitals only have 2 beds per room.
Medication prescribed by a doctor is covered by compulsory health insurance if the medicines are on the List of Pharmaceutical Specialties published by the Swiss Federal Office of Public Health. When a generic alternative to a brand-name medicine is available and you opt for the brand-name product, you will have to cover 20% of the cost yourself. When no generic alternative is available, brand-name medicines are fully covered.
3. Ambulance transportation
The biggest downside of not being able to obtain supplementary health insurance, in your case, is the fact that compulsory health insurance coverage for ambulance transportation is limited. It only covers 50% of the cost of ambulance transportation, up to a limit of 500 Swiss francs when the condition is not life threatening and using other forms of transportation is not possible, and up to a limit of 5000 francs when the condition is deemed life-threatening.
You will always be able to obtain emergency medical transportation (even if you did not have any health insurance coverage), but without supplementary insurance you will have to cover 50% of the cost. What is more, emergency medical transportation outside of Switzerland is not covered at all. In some cases, such as when helicopter transportation is required, the uncovered portion of costs can be substantial. Transportation between hospitals, once admitted, is covered by compulsory health insurance when it is ordered by doctors.
Swiss supplementary health insurance policies cover all or part of the ambulance transportation costs which are not covered by compulsory health insurance, and may provide coverage for emergency medical transportation outside of Switzerland and repatriation to Switzerland. This coverage is provided by many travel insurance policies as well, and obtaining a travel insurance policy is generally easier than getting supplemental health insurance. However, it is important to note that both supplementary health insurance and travel insurance policies may exclude incidents resulting from pre-existing conditions from coverage.
Best regards from Moneyguru
More on this topic:
Swiss health insurance: 16 costs covered by your compulsory policy
Getting medical treatment outside of Switzerland: What does Swiss health insurance cover?
Emergency transport, search and rescue: How to insure the cost