Your Legal Rights
You are entitled to union representation at every participating site where you work, including the VA.
There is a difference between failing to progress academically and misconduct in the employment relationship. Often, there can be some overlap. You are entitled to union representation at ANY investigatory meeting, but you MUST ask for it.
Whenever a person in authority begins to ask you questions that you reasonably believe could result in a disciplinary action, you have the right to refuse to answer questions until a union representative is present and you have had an opportunity to discuss the situation with that representative. You have a right to have the union representative present during questioning, to have that representative advise you, to ask your supervisors for clarifications, and to ask for any additional information after questioning. These are referred to as your Weingarten Rights.
Is asking for representation awkward? Yes. However, it's the prudent thing to do. If you are asked to attend a meeting and not given a specific reason for the meeting, assume it's investigatory in nature and respond that you'll be happy to attend with union representation. It's unfortunate that the reason for a meeting isn't made clear to you, maybe they call it a "touch base" or other non-threatening term, but the purpose of the meeting is to investigate allegations. Contacting the union after an investigatory meeting isn't going to be as helpful as getting the union involved initially.
The union exists to ensure that you are treated as fairly as possible, but we can't put the toothpaste back in the tube! When in doubt, reach out to the HOA!