The uncle wants us to go there, or The uncle wants that we go there? The uncle wants to go there would surely be " ο θείος θέλει να πάει εκεί"
I put 'Ο θείος θέλει να πάμε εκεί' but it marked me as wrong even though it gave that as the right answer.
There are a no umber of sentences with relatives in the abstract (the uncle, the mother, etc) which is awkward in English. Whose uncle? A native English speacker would surely identify the uncle (their/her/John's/my/etc uncle). I know the Duo sentences lack context, but could this be a real sentence without a possessive? And if so, are we supposed to understand an our or my from the subordinate clause?
if i were to want to show "us" in the sentence, where would I put it?
You mean emphasizing it? Because it is already present in πάμε= we go. If you would like to emphasize it you can say "Ο θείος μάς θέλει να πάμε" or "Ο θείος θέλει εμείς να πάμε=the uncle wants (that) we go"