Hi Dominic, these sentences have all the same meaning, but I would use:

- I'm glad... mi fa piacere che tu abbia dormito di nuovo

- I'm happy... sono contento/felice che tu abbia dormito di nuovo

I would use subjunctive after "che", but I know that it is an intermediate/advanced grammar topic.

Thank you Antonio. Do they have no difference in meaning or one would be better in certain contexts? (I haven't really started subjunctive yet! :-) )