Here is a link to a policy briefing written in 2009 by Julia Brophy and Ceridwen Roberts (University of Oxford) which compares the law relating to access to family courts in a number of jurisdictions (Australia, Canada, New Zealand and Scotland). The law is not all up to date, of course, but it may still be helpful as a starting point in looking at what happens elsewhere. (Copy also uploaded with this post.)
(Amended to include a link to the Nuffield page. You can also read a briefing on the proposed reforms in 2010 there)
(Amended 11 January to add this link to the Child Court law reporting project in Ireland which includes a detailed report written November 2014 on its Interim Reports page.)