Answer: The upright branches you describe sound like suckers and they can be pruned off without harming your tree. Or, you might try weighing them down when they first appear to help them grow into a more weeping habit. I've been known to tie rocks on the branches of my weeping cherry tree to make them hang down. Either way, you won't hurt your tree. As for the long branches at odd angles on your other tree, I'd prune those out, too. You can do all sorts of pruning with trees to make them look better. The only rule to follow is to try not to take off more than one third of the live growth (pruning off too much at one time can really stress a tree).
Best wishes with your landscape!
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