Hi, I'm Robert and I'll be helping you with your financial software question.
Yes you can just delete one account without affecting the other
You need to take a look at the accounts. What probably happened is that quicken didn't recognize it as the same account and so it created a new one. Quicken does that frequently.
Most likely the new account only has transactions going back 90 days. But that is the account that quicken will continue to download to if you continue with the express connect. So if you delete it you may just have it pop up again. If you delete the original account you will lose your transaction history older than 90 days.
What you really want to do is go to the old account. highlight all of the transactions before the first transaction in the new account. Right click on them and select MOVE TO ACCOUNT. Then select the new account to move them to. When that gets the new account complete you can delete the old one.
I Strongly advice making a backup of the data before doing this as it is pretty easy to make a mistake and if you have a backup you can always restore the backup and try it again.
I have an Apple Mac Book that I have just started using, no right click, than where does MOVE TO ACCOUNT appear
try command click on the mac. but essentials is different it might not do that. I think it does and usually command click works the same as right click on the mac