Proof for variation of Prim's and Kruskal's to find maximum-weight acyclic subgraph
This is a nice exercise.  You should probably do it yourself, to get the learning benefit.  I suggest that you enumerate all non-isomorphic graphs with 3 vertices or 4 vertices, and for each such graph, try playing with the weights to try to find a counter-example.  Basically, keep trying what you've been doing, but be more systematic and exhaustive about it.  You're on the right direction -- keep at it.