Asking for someone's signature seems like such a little thing, yet there is a social etiquette that goes with this favour, especially if asking a superior outside their office. Many years ago, I got a professor's signature at a party. Though the party was on-campus, I was busy elsewhere at the school and did not attend. When I realized I needed his signature, I took a pen and the form and caught him in the middle of the crowd at the party.
He frowned at the request but when I presented him with the pen he signed. Since I was a graduate student in his department, my professor was not in a position to cut the relationship. However, you indicate that with your former manager you want to firm up an already shaky relationship--you don't want her to frown. I looked online and found advice from secretaries and others regarding What is a polite way to ask for a signature from your supervisor or a boss?
Ann Bartlett, a person who worked at a vet clinic while in school--and presumably needed a recommendation from her employee to get another job, writes in part:
If you need something signed to confirm that you are always on time
for work because you are getting another job then just be polite and
try to break the news to your boss gently. They may not like your
decision [to get another job] but that is the way of the world.
From a secretary Melissa Hoy:
I often need signatures from one or both of the owners. I just walk
into their office (if they aren’t in a meeting or on the phone), make
sure they are done with whatever they were doing when I walked in, and
tell them “This is...and I need you to sign here” pointing at the
signature line with the pen I have brought with me so they don’t have
to hunt for one.
Nearly all of the answers are for office settings but the central message is to make it easy and convenient to provide a signature.
Since asking my former professor's signature at a party, I've had some training and experience for asking favours outside the office setting. Because yes, providing a signature outside the office is a favour. In my experience, people like your former manager appreciate being asked privately before the event how they feel about providing their signature at a social. You might send her an email along the lines of:
I am pleased that you have accepted my invitation and I don't want to
further impose on your free time. However, at some point I will need
your signature for my professional certification. Time is of the
essence because I am moving overseas for the rest of the year. I can
bring the form to your office sometime, or I can bring it to the party
if you wish, or meet with you otherwise at your convenience. Let me
know what works for you. Thank you.
That will let her know that you value her time and services enough to make the necessary sacrifice to obtain her favour.