There are a few pieces of information that I would need to know to give an exact solution, however, I'll tell you what you need to do and I'm sure you can figure out the rest. Either way you'll need to start with a transform project. You can use either the Tuner or the Editor. If you're using the Editor select File->New, and select a Transform project.
First, what you want to do is re-set the current cached data dir. You'll need to know the property name of this path inside the original msi. Let's call it CACHEDATA_DIR. You'll need to track this piece of information down and substitute the correct value. If you don't know the name, you can track it down from either a log file or open the .msi within Orca and look at the Directory table.
Second, if the original install prompts for this information then you're job has gotten a whole lot easier because this can be handled within a response transform and you don't need to know the above information. When the transform project opens select 'Response Transform.' The rest is filling in the blanks.
If this isn't exposed through the original install, then you've got a little bit of work. Look to see if the directory name is exposed anywhere in the .msi (via the transform project). You really need to find the original property. Once you find where it's defined, change it and save the results in the transform.
Finally, if the transform project doesn't show this property you'll need to make the changes by hand. Thus, the very hard way...
1. Create a new CA, RedirectCachedDir and give it a type of 51. The Source value will be the existing property CACHEDATA_DIR and the target property will be the new property, let's call it NEWCACHEDATA_DIR.
2. In the directory table, create an entry for NEWCACHEDATA_DIR. From what you described it'll be an addition to the [AppDataFolder]. Populate the columns as necessary.
3. Add the NEWCACHEDATA_DIR custom action to both the InstallUISequence and InstallExecuteSequence prior to CostInitialize.
Save the transform and give it a spin.
Hope this helps,