I tried researching it and and found that probably (according to some people on Internet, whose authority I can't confirm ) both come from latin expendere
True. But audio is disabled, it won't come as a listening exercise. At least that.
Would the verbal noun construction work here? I thought "I like spending time with you" would be "lubię spędzanie z tobą czas"? To me, "lubię spędzać z tobą czas" translates to " I like TO SPEND time with you".
I know there is little to no difference between the two in English, but verbal nouns are used in Polish when we use such sentence structures.
"I like to spend time with you" works here.
"Lubię spędzanie czasu z tobą/z tobą czasu" would feel weird to my ear, although I can't say that it's wrong...
Is there any particular reason why it's not "Lubię spędzać czas z tobą"?
It should be accepted. Pronouns (z tobą) are usually not put at the end of a sentence in Polish unless they are stressed, so the moderators do not usually include them in the solutions, but I think this is an instance where emphatic word order would be possible and should be accepted.