how can I change a website for investments in my vault

Unknown

my brokerage website changed.  Do I need to delete the old website or can I change it to a different website and keep my investment history?

Vetta

You will have to change it. It will require deactivating/reactivating the account for downloads. With the first download link it to your existing account (I am assuming the website has changed but not the broker).
If this is a new brokerage you will want to start a new account, but your holdings can be transferred into it to keep cost basis history.

NotACPA

Deactivate EVERY account with that old link.

Exit Q, Restart Q (because Q sometimes remembers things, the Exit fixes that)

Reactivate any account with that brokerage.  This should cause ALL of the accounts to be made available for download. 

MAKE SURE that you correctly identify which online account goes with each account in Q ... THEN, be sure to use the dropdown to NOT select ADD (the default) but instead choose LINK, to your already existing account(s),