For a few years I had an adopted daughter on an Indian passport. Until the adoption authorities here recognised the Indian adoption I couldn't get her an irish passport.
this meant i had to apply for visas whenever we went to various EU states.
The problem is that every state has different visa procedures -and ,worse, they changed every year. The irony is that the EU visa or,rather, Schengen visa should allow entry into all states who've signed Schengen AGreement. And yet each Schengen state has a different application policy.
For example - we often went to Spain. For a couple of years no problem at the Spanish Embassy - a small wait ,handed in the application form and got the visa. Then things changed one year which meant a long wait at the Embassy, and had to wait a few weeks for reply.
So,instead I applied to Portugese Embassy. Very quick. And thus we were able to travel into any other Schengen state, including Spain- an hour from the Portugese airport.
In one case -Italy - the visa guy said "we have to interview here". I said she's only two and we have all the proof that we are looking after her. Doesn't matter -every applicant for a visa into italy must come for an interview.
So we got a visa from the French and flew into Nice -30 mins drive from italy and drove in.
So, the moral of the story is - phone each Embassy here in Dublin, find out which ones are the quickest/easiest visa policy. Some are awful, some less so.
Once you have the Schengen vuisa you can go from one Schengen state to another.
The above is based on 1996-2004, so things may have changed since then-PLUS this was based on an indian passport holding child, not a S.African one PLUS the child is legally yours whereas at the time nobody but the Indians recognised our daughter as our child-she was purely regarded as being in our care.