I think in the end you have to remember to do what is best for you. Is there anyway to have them both under your care for these next few months until that child leaves in september? I should back track a little, would this new family be starting in september? or much sooner? If it is for september than I would tell the relocating one that "due to the knowledge of their potential leave in september you had to ensure your continued financial stability and had to make a decision to accept a new Family under your care for that time Frame. So their last month of care would therefore have to be x.........
Because you just can't have things all up in the air. Its not fair to you. Parents are often just thinking about themselves and what is best for them and their child. But you have to think about you and whats best for your income. This just forces them to have a more concrete exit date so that they DO start looking and don't spin your life and income into the unknown closer to their moving time. The way I see it is you have to think ahead of their plans. You haven't been put on this planet to work just for them. Ideally I would try to be fair and care for their child until they actually moved, so that they could start at the new daycare the same month that they'd be starting to live in their new place.
But I do like Inspired by Reggio's points.