I'm looking for any opportunity to to track social mobility across generations.
This does not sound like panal data to me. It is a very classic problem in sociology and all that is required is to have parental education or class and the respondent's education or class. A simple survey like the General Social Survey (http://www3.norc.org/GSS+Website/) in the USA or the ALLBUS (http://www.gesis.org/en/allbus/allbus-home/) in Germany is sufficient, and a lot easier to work with.
the panel study of income dynamics is the authoritative source for this information
the national longitudinal surveys also have detailed questions about this, but for a shorter cohort.
For international comparisons of intergenerational mobility commonly used datasets are the International Social Survey Program (http://www.issp.org/) (in fact, both the GSS and ALLBUS mentioned above are part of the ISSP) and the European Social Survey (http://www.europeansocialsurvey.org/).
For a list of such datasets in many countries, see the project International Stratification and Mobility File (ISMF) by Harry Ganzeboom and collegues (http://www.harryganzeboom.nl/ISMF)