Green hydrogen production is necessary for the green transition. However, producing green hydrogen at low cost and low CO2 emissions can be challenging in day-to-day operations of a grid-connected renewable energy system. Therefore, this research introduces an extension to a recent co-optimisation method that relies on long-term and daily planners that consider past data and short-term forecasts to plan hydrogen production. The extended method allows the long-term planner to minimise cost while the daily planner minimises CO2 emissions, and vice versa. The extended method has the potential of reducing the levelised cost of hydrogen when the long-term planner minimises the CO2 emissions and the daily planner minimises the cost. However, the cost reduction relative to utilising the same objective by both planners is not guaranteed because of the intrinsic nature of planning with short foresight into the future. To achieve the lowest CO2 emissions, both the long-term and daily planners should aim for the same objective of minimising the CO2 emissions. The findings suggest that prioritising the reduction of CO2 emissions from hydrogen production may be a better option as the benefits of generating additional green hydrogen could likely offset the loss of potential revenue from cost minimisation strategies.