Complex sentence: The Association, which refused to agree to this at the time, had begun organizing and mobilizing for a potential strike as talks entered mediation when the District claimed it had reworked its budget and was prepared to return to the bargaining table.
Split into simpler sentences: The Association, which refused to agree to this at the time, had begun organizing and mobilizing for a potential strike as talks entered mediation. Shortly therafter, the District claimed it had reworked its budget and was prepared to return to the bargaining table.