What do I say?

[Lee-Bee]

I not understanding fully.

So you limited to 5?
You have contract to start 2 before the two they replacing leave?
Do you not have notice with firm end date?
Or if these new ones replacing aging out childrens, did you not know when school starting?
I just think odd that the one parent who been in care, not knew, and not leaving, is the one be denied care on overlap day. Surely of all children, that one's place should be assured since she is the constant.
I do understand it been big pain with her level absence especially when they not pay but if those your terms, I would be annoyed if my child's carer suddenly asked me not come one day because it inconvenience those leaving and those just coming in! Surely if they contracted for place, it should be avail to them. What if Mom is already in trouble at work having so much time off with her sick child? It seem if she been home for almost month in the last 3, then another day off might be last thing she can get.
Likely you knew for some weeks that this day might be issue. What would you do if this child not been out sick so often?
How were you planning on deal with over ratios when new contracts were signed before knowing leave dates?
Since you want this client to stay until you transition two new ones, and then are opening the place up, why risk this parent get cross when care denied on Wednesday? It seem like new persons have more consideration than existing client. Mom might think that too.
Why not ask parent of child going school on Thursday to have extra day home? It seem maybe she not give firm leave date and with her child not going school as expected, it is maybe why new child contract for start was too soon?

It is not uncommon for JK to have a staggered start around here. Some children do not start full time until the last week of September. So planning for a new child to start can be a bit tricky if the child leaving ends up being one of the later children to start school. I suspect this is what happened here (but with only one over lapping day, luckily).

While I agree that the newest child to start should be told there isn't room on that day...it isn't unreasonable to ask the family that has been keeping the child home frequently if they are able to keep that child home. They just can't be penalized for saying no. They shouldn't be told they can't come that day. But it is totally reasonable to ask the family to help out if they are able and willing.