Is it ethical to present a second paper at a conference when the first paper and travel was funded by a separate organization?
I can't see any ethical issues at all. You seem to be properly fulfilling the obligations of your funding. What else you do at a conference is your own concern. The funders are willing to support you and you are doing what is required for the funding. Rest easy. 

I can't imagine that any funding agency would suggest (or even think) that you can't do other things at a conference. They certainly expect you to take advantage of the opportunities it affords.