BEDIT edits the block in the one drawing file you are in. You are thinking of XREFs instead: do you need to use XREFs for this situation?
PLUS Toolpalettes are static: like having two copies of a book, one on the shelf (aka Toolpalette) and one in your hand. remove or add pages to the one i your hand will not change the book on the shelf.
So... find the original source of the Toolpalette block (you have to edit the source), then move it to the TP to replace the one you no longer want. You need to maintain one source for all your blocks: they want you want to do it will create one heck of a mess whenever you need to fix things again.
Now back to your other question: LT does not have a block replace feature, so you are going to have a hard time doing what you want easily. Your choices in LT are:
1. Rename the old block and INSERT the new block in it's place at every location.
2. WBLOCK the revised block out to a central location with the same exact name then use INSERT command to replace the one you have in each file.
Good luck.