Their HR dept seems to not have the ability to onboard people without their HR system and the answer to any query is “system says no” rather than just simply emailing on the Garda vetting form.
So the key question is; is this an indication of the company as a whole or just HR. If she knows who her new line manager is going to be it may be worthwhile talking to them to say things are not going well with the onboarding and HR seem to loose docs, not answer queries, or are in general not helpful. Ask the manager if this is typical of the company culture. Find out now if there are red flags or if it is because of a short term issue.
I have not been too impressed with my companies systems for new staff and have not been remiss in pointing out to HR that this is a first impression for new staff and they have to do better.
A lot of organisations are disorganised. So if she wants to come back, she is probably going to find that the company she works for is disorganised. I suspect that the charity sector is less organised than the private sector simply because there would be much more oversight and the private sector would be quicker to get rid of deadwood staff.
I've worked for several private companies, including a few large publicly quoted multinationals, who exhibited similar inefficiency and dysfunctionality when it came to hiring, managing and firing employees. In fact, such inefficiency/dysfunctionality was a significant contributory factor into my decision to quit the industry and effectively take early retirement.
The typical charity in Ireland is something like services for autistic children in Co Limerick. Small, and limited to a specific task with geographical boundaries.