Pushing is fine.
Stay away from swinging as much as possible. You can knock a shield out of the way some, but it can be hard to do this without hitting the person behind it.
If you're really wanting to agressively bat shields/weapons/fighters out of the way, get a glaive.
The holding sideways thing sounds like a crosscheck, which is fine, with a couple caveats. Basically, try to use it against their shield, and try to keep it relatively low. If you hold it sideways high, it WILL (maybe not every time, but sometimes for sure) smash the other fighter in the face with your unpadded haft, which really sucks. I would try to stay away from doing this on unshielded fighters, as you should be stabbing them in the gut if they rush you anyway.