I don't think that you do Eliza - sorry for giving the impression that I did, but much of what you are describing is taken by many to be how "real Gypsies" should be, and castigate those who aren't, which creats problems.
We've been on idyllic sites (especially when its not raining) where Travellers have been given a reasonable site and good facilities and are happw where they are - the Winterbourne site outside Bristol was the last time we worked in depth with a singer - magic!
However, our main experiences were in urban settings with rat-infested sites with no running water and sanitation, constant harassment by the police and a permanent fear of having bricks, or even fire bombs thrown through their windows.
The John Major Government did away with the legal requirement for all councils to provide sites and Travellers today are no longer protected by the law as far as having something as fundamental as having a place to stop is concerned.
Things are ten times worse in Ireland - in our town, the police have been known to visit all the pubs when Travellers are seen in the area and instruct the publicans to lock the doors and only allow people they recognise onto the premises - failure to do so means that police will not respond to calls for assistance should trouble break out.
"their own name for themselves"
I'm always a little wary of this - I'm well aware of the different origins of various groups of Travellers, but I've seen far too often these differences being used by Gypsies "It wasn't us - it must have been the "tinks, nackers, pavvies, mumphers..." or whatever abusive term people have for non-settled families.   
English Gypsies were notorious for this sort of scapegoating prejudice at one time.
In reality, there are very few pure-bred Gypsies nowadays - there haven't been for along time.
Today's Travellers all face the same problem - getting a decent stopping place and being treated as human beings.
Sorry to have given the wrong interpretation of your views and experiences, if I have - just coming to the end of a very unpleasant argument with someone who is supporting the ethnic cleansing of Israeli Bedouins - it's left a nasty taste in my mouth
Best wishes
Jim Carroll