Complex sentence: Eleonora, through her father, provided the Medici with a powerful link to Spain, at that time ultimately controlling Florence, providing Cosimo I with the opportunity to show sufficient loyalty and trust in Spain for the withdrawal of Spanish troops from the province.
Split into simpler sentences: Eleonora, through her father, provided the Medici with a powerful link to Spain, at that time ultimately controlling Florence. The union provided Cosimo I with the opportunity to show sufficient loyalty and trust in Spain for the withdrawal of Spanish troops from the province.