Your Chairman’s right, because as an alternative to the conventional “sit-down” Meetings, Executive Committees (EC) may have “virtual” Meetings (e.g. telephone or email), and can even have no “Meeting” at all provided the Secretary produces written Agenda including proposed resolutions to all items shown, and obtains the written approval of those resolutions from a majority of Committee Members.
So if the Chairman of your EC refuses to convene a “sit-down” EC Meeting, a written request (a “requisition”) including the Items to be discussed (e.g. expenditure, removal of the Strata Manager), and signed individually by a minimum 25% of Owners (by Unit Entitlement) will require the convening of a General Meeting (GM) of Owners
With regard to your Plan’s expenditure, that’s a function usually delegated to your Strata Manager under the provisions of the Agency Agreement; with limitations.
A standard limitation is that except with the prior approval of Owners at a General Meeting, no payment may be made against any item that would bring the YTD spend for that item (e.g. grounds maintenance) to an amount that would exceed its approved annual budget allocation, plus 10%. Further limitations, or a decision to have none at all, must be resolved one way or the other by Owners at each Annual General Meeting (AGM). You would need to check the Minutes of your Plan’s last AGM to ascertain which if any restrictions on spending apply.
So far as removing your Strata Manager (SM) is concerned, before submitting the “requisition” for the GM, you should check what termination conditions apply under your Plan’s Agency Agreement (3 months written notice is normally required), and then move to place an Item on the Agenda for that GM in those terms.