Second author being lead presenter on paper at a conference?
As far as I see there is nothing particularly strange with any of the authors presenting while any other authors also attend the conference. (Well, I am from mathematics where there is no such thing as "order of the authors" but I also work with people from other disciplines which do have this notion.)

So having the second author presenting while the first authors is in the audience seems totally OK for me. (It could just be that the presenting authors is the "best presenter of the group" or, by contrast,  should train presenting…)

Also it is totally OK for you to be first presenter, especially since the student agreed. There are many different things influencing who presents some paper/poster (some of which you already stated such as funding, time to attend) and I think the audience would not even think about the issue much. In general, all authors should discuss who should be presenting and as long as all authors agree, the outcome is OK.