In the following sentence, The men were both caught cheating at cards, what is the right representation of "cheating"?

TP-> DP + Tbar
DP-> D + N
Tbar T + VP
VP-> QP + Vbar
QP-> Q + DP
Vbar-> V + PP
PP-> P + DP
DP-> D + N

Is the representation of Vbar correct?
How could "cheating" be part of V while "were" = tense & "caught" is VP CORE??