Thanks for the clarification. In general, I recommend working through the "How to Interoperate Inquisit with Online Survey Packages" topic in the Inquisit documentation (specifically the use of query parameters is important). The "How to Combine Multiple Scripts" is also useful. The general flow you'll want to use is something along the following lines:
(1) Start with a simple Qualtrics landing page. Let Qualtrics generate its unique participant identifier (you'll want that to be able to easily match collected data between Qualtrics and Inquisit) and have send people to the Inquisit experiment's launch page. Have Qualtrics include the unique identifier as a query parameter *and* another numerical query parameter which you are going to use for condition assignment (i.e., the different order of IAT scripts). In your case, that 2nd parameter should take on values 1 to 4 in equal proportions (you should be able to configure this via Qualtric's quota management, I believe). As far as I am aware, query parameter handling is covered under the term "embedded data" in Qualtrics, but you'll want to check their documentation in case that's changed.
(2) Your launch page must be set up to capture the two query parameters (you do so via the Web Script Wizard). You'll want to use the unique token as subject id and the 2nd numerical parameter as group id. Register the script containing the <batch> elements as your active web script and be sure to upload the actual IAT scripts and all their dependencies in the next step of the Web Script Wizard. The "batch" script should read along the following lines:
<batch>
/ subjects = (1, 2 of 4)
/ groupassignment = groupnumber
/ file = "IAT_A.iqx"
/ file = "IAT_B.iqx"
</batch>
<batch>
/ subjects = (3, 4 of 4)
/ groupassignment = groupnumber
/ file = "IAT_B.iqx"
/ file = "IAT_A.iqx"
</batch>
To launch, for example, the second order (IAT_B first), Qualtrics should forward participants to
http://research.millisecond.com/username/mybatch.web?mysubjectid=someuniquetoken&mygroupid=3or
where 'mysubjectid' is the unique participant identifier and 'mygroupid' determines the order of files to serve. You'll probably want to use both an odd and an even group id (here 3 and 4) to refer to a given order of files because the IAT scripts themselves *also* use the group number to do condition assignment (i.e., determine the order of blocks; compatible first vs incompatible first as determined by even vs odd group ids).
Note that in the scenario sketched above, the order of blocks would be identical in both IATs. If you wanted to avoid that, you'd have to make additional changes to the IAT scripts.
(3) Finally, via the Web Script Wizard, have Inquisit redirect your participants back to Qualtrics. Have Qualtrics pick up where it left off, serving the demographics questionnaire.
All of this sounds more complicated than it actually is. I thus recommend just giving it a try.