I know it sounds weird, but I don't want the transcript office of my US alma mater keeping records of where my transcripts were sent.
The reason is I don't want people I know to call the transcript office pretending to be me and get the names of schools I applied to.
If you're in the US, talk to your registrar about what we call a "Privacy Lock." It is pretty much a set of measures to apply should the students wish to remain private. Things as extreme as taking you off the online directory, conceal all your names and e-mails, etc. can be done. Each school may do it slightly differently so you'd need to talk to them and get a sense of what is covered.
As for the transcript recipient, you can actually try asking them to put a flag in your personal profile. Most school registrars will probably open up your online record should someone call and ask about you, and if they see the flag they will know how to act accordingly. You can discuss with the registrar on what kind of privacy measures are in place by default and see if additional flags is appropriate, such as "do not disclose information unless in a face-to-face meeting with official proof of ID," etc.
And lastly, you may have to learn about the same security measures in your next school as well, perhaps as soon as you're enrolled. A lot of information is put online and I personally think it's exhausting to make sure that your name will not be featured anywhere. For instance, what if you applied for a scholarship and got it, and the funding agency wants to make a press release? What if you wanted to publish a paper and the journal needs to know your name and affiliation, and will print them if your work is accepted? Somewhere somehow they may still be able to find you so you'll need to be prepared.
And whatever that is driving you guys apart, I wish you'll find resolution and peace soon.
While this might depend on the country, I would think unofficial transcripts would be suitable for the initial part of the admissions process. Some schools may require an official transcript prior to officially offering admission. I would ask whoever is writing a letter of reference for you to include a copy of your transcript with the letter. The letter should briefly explain the situation.
Any school that is not willing to help protect your privacy during the admissions process is probably not a good fit for you in the long run as they may not be willing to protect your privacy as a student.
That said, I am not sure what you are protecting against. I am not sure what damage knowing where you applied can cause.