Upvote:1
The best thing to do is, after arrival in Germany, is to go to an Apotheke and get an EU Vaccination Certificate issued (which would be issued against your passport/id) if they are satisfied that everything is ok. (Showing your marriage certificate will definitely be helpful)
Make sure that your name and birthday on the issued certificate matches that in your passport/id!
The certificates are issued independent of citizenship or residence status and are free of charge.
An Apotheke will more likely know how individual national certificates from other countries looks like. The yellow International Certificate of Vaccination booklet should be no problem at all, since they are commonly used here.
Not all Apotheke issue these certificates, but one can be easily found here:
If you supply them with your email address, they will also send you a PDF of the certificate (otherwise you may only get it in a paper form).
Installing the CovPass application, which can also create a PDF, beforehand would also be a good idea, since then you only have to read/scan in the QR-Code of the printed EU Vaccination Certificate. An English version may be installed when downloaded from non German stores or on non German language phones/tablets (haven't tried this myself, so confirmation would be nice).
The application can store certificates for multiple peaple.
For the relevant German legal text for the issuing of the EU Digital COVID Certificate, see my answer at: Are there countries that allow tourists to obtain the EU vaccination certificate?.
When restaurants checked at all (I, personally, have never been checked up to now), most of those checking will more likely accept something they are familiar with. They are also supposed to check that the name and birthday matches that in the passport/id.
Fines for them could range anything between β¬ 1000 to β¬ 5000.