In phrase 1, "an seanteach" is not the object of the verb, it's the object of the preposition "ag". In phrase 2 "na doirse agus na fuinneogaí [there should be no lenition]" are the objects of the verb "péinteáil" and "an áit uilig" is the object of the verb "glanadh". So the two phrases are not equivalent to each other. Generally in a non-finite clause the object precedes the verb, but a prepositional phrase can come after the verb. In case anyone is confused, in Standard Irish the sentence would be: "B'éigean a ghabháil chuig an seanteach arís anuraidh agus na doirse agus na fuinneoga a phéinteáil agus an áit uilig a ghlanadh."

What I say to my students (who are young and don't want to hear about objects) is that verbs are bullies and the first one pushes the second one to the end of the sentence. The second one then changes how it looks to avoid the bully (to account for the fact that the second one will look different to how it usually looks: déan --> a dhéanamh for example). Then later I'll introduce the verbs who come along with other words and explain how bullies are afraid of groups. Like this sentence: Caithfidh mé féachaint ar an teilifís. In that sentence féachaint didn't run away because of his buddy 'ar'. And only réamhfhocail are good buddies in this instance but that's another story...