Cloak or mirror all links from one website to another?

thanks in advance for any suggestions. Here is what I'm trying to accomplish, if possible.

I have 2 domains, e.g. www.domain1.com & www.domain2.com I want to redirect visitors from www.domain1.com to www.domain2.com without the users knowing that they are going to www.domain2.com.

So far, the easiest solution is domain cloaking, which achieves the above.

Now, I'd like it so that every time someone accesses domain1 and gets redirected to domain2 under a cloak, when they move their mouse over a link or click on it, it doesn't display www.domain2.com/directory, but either a static www.domain1.com link or a mirror of the directory but displayed as domain1.com/directory

Is this impossible? The situation is aoying and if circumstances allowed, I wouldn't be doing this at all.