"She has now got very upset with me and has said she can give herself admin time as and when she feels she needs to."
No, she can't. If it's a committee-run playgroup then the committee is in charge. The manager can't just decide to pay herself for extra hours, especially if she won't even tell you what she is doing.
You need to be able to plan ahead and budget for each coming term or half-term. You can't do that if you don't know what the staffing costs are going to be.
Another potential issue is that if she is refusing to delegate, this could end up costing you/the playgroup more. If she's paying herself at a manager's hourly rate to do a job that could be done by someone on a non-managerial rate, it's obviously going to be a more expensive wage bill.
It's highly likely that there is a lot of work to be done outside of playgroup hours, but you/the committee need to know what it is. It might be that it's something that could be done by committee members - or you might prefer to pay her so that it's not left to volunteers.
A committee chairperson (or another member if required) would usually be expected to hold an appraisal meeting with the manager. (The manager should be doing the same for the other staff members and reporting back where necessary).
The idea is to use the time to discuss how she/the committee feels things are going and what could be done to improve things. Issues raised could include things like the manager wanting staff to attend particular training courses, or things to be done in a different way. This would be your opportunity to raise the admin issue. As an employer you also would be looking at the possible effects on the staff if they are having to work outside of their usual hours.
It may be that things are being done purely because it's the way they've always been done rather than because they are actually needed.