If it is not letting you move into a contested hex in move mode, that could be WAD. Not that I know, but it would make sense that you can't move into a hex with an enemy LCU in move mode.
No such design. You can move into contested hexes (if all other parameters fit).
I do it all the time to speed marching up, and when my troops are about 20 to 30 miles - depending on road condition - from the enemy I switch to combat.

