Re: Rheinfelden hospital
Yes, very wise. I used to live with a nurse here in Switzerland, and she told me to always avoid the smaller hospitals!
You should register soon with the Uni hospital in Basel, and maybe meet your midwife, so they are ready for you. The first baby usually takes a long time, so no need to panic on the day. After the birth they will need to see your papers, both passports, and will register the birth for you. Ask for the international, multilingual birth certificate.
Don't forget to arrange health insurance early enough for the baby, you only start paying when it is born. Otherwise you will be liable for baby costs until you get some insurance...