I need to use IE to log into 2 specific URL's and then Chrome for all others. Is there a specific way I can make this happen?
No, there is no practical way to do that. Windows has a list of “handlers” which tell it what to do (eg what program to run) when different types of files and system objects are activated (eg opened).
The list is limited to types which for the most part just includes extensions (eg .EXE, .DOC, .URL, etc.) There is no way to specify handlers for specific filenames since the list would eventually grow ridiculously large and provide extremely poor performance. Worse, there is definitely no way to specify handlers based on the contents of a file since that would require Windows to (1) open the file, and (2) know how to read and interpret the contents.
The easy way to help you deal with specific URL's is to create a shortcut for one URL that opens IE to access one bank and another shortcut to use Chrome to access another. But this will not work with links in an email. It will only work for pre-know URLs.
If you have always wanted an excuse to send more money to Steve Jobs, you might want to buy a MAC if you have a great need for this type of option. There are "pay for" applications for a MAC that when you open a link it will give you a list of what browser you want to use. However I understand this type of application requires you to specify a browser for each link you open.
I think the shortcut is a good solution.