If she previously paid into the German state system (not really a state system but for want of a better word - in German it'd be a "gesetzliche Krankenkasse") then I think she can be taken back into that system without penalty of any kind or without being forced to take private insurance. [edit: see that PeteD already mentioned this, sorry, missed that first time round]
There are some international private insurances which are recognised in Germany, but not many. I'd recommend losing a few hours of your life to the
toytowngermany forums. Obviously, it's a Germany-based website (for English speakers) but given your connection to Germany, it's probably not a bad place to start. There are a few insurance guys who contribute a lot to the forums (users Starshollow and John G. in particular) who are extremely helpful. I don't really participate over there any more but there are
wiki pages here that are useful and here's one link to a
discussion on international health insurance. Seach health insurance and you'll get loads of results (use the google-powered button for best results).
With regard to the EHIC, that's really only intended as a way to get health cover for short stays in EU countries that you're not resident in. So it's handy for holidays but not meant to replace health insurance in your normal country of residence. For example, sometimes the only things covered are emergency treatment and/or pain relief to get you through your holiday and back home. I chipped a tooth once when on holiday in Germany while I was actually still living in Ireland. Went to the dentist in Germany with my E111 form (which the EHIC replaced) and all she could do was give me pain relief and a temprorary filling. Nothing else was allowed at the time - I had to wait till I was back in Ireland to get the proper work done.
I'd be inclined to say Ireland would definitely not be one of the best options to choose for you as the whole system there can be a bit ridiculous. But there are lots of discussions among some very financially savvy people on
askaboutmoney.com if you wanted to inform yourself about how things work there.