The wedding planner sounds so frustrating
You may have done this already, however I would set up a meeting with them and yourself and FH, with a clear list of their responsibilities in say a spreadsheet. Make it very clear to the planner what dates each task needs to be completed, and get their input and agree together on a date for each item. Then keep all those dates in a spreadsheet, and update and send it weekly to the planner. That way you really have documented everything they say and they have less of an excuse to delay things!
I work as a project manager and I find this trick works when people working for me are not doing what they promised, or dragging the job late.
Let me know if you want some spreadsheets