while waiting for Barry to respond to your post, let me help out with some of the questions.
to our knowledge, H. pylori is not related to skin disease. some people claim that it is and after antibiotic treatment, they are cured. but, the it could be any bacteria and was eradicated with the same antibiotics. I believe that H. pylori only relate to gastrointestinal problem.
I am sorry to hear what happened to your father. From literature, we have higher chance of catching H. pylori from mother than father. However, it really depend who really take care of you when you are young. I believe you would catch the bacteria from whoever you spent most of your time with during childhood. not necessary to be your parents. could be your grand parents, babysitters or day carer.
as for your daughter, if she is old enough, can get her to do some test and see if she is infected with H. pylori. if she is young and the symptom is not too severe, can wait till she is older.