I know what you mean about feeling badly but in all honesty, I have simply decided to take on the state of mind that this (daycare) is a business and businesses don't often "feel" anything other than needing an income.
Once you take the personal aspect out of it, the rest comes easy. I AM friendly and chatty with my DCP's but ANY financial or policy talk means that I follow my rules so I expect parents to do so as well.
If this part time family KNEW that you charge per space NOT attendance then they should be fully aware that they owe regardless.
If they don't respond, send them an invoice stating their balance along with late fees if your policy dictates it and mention that there will be no further services until ALL balances are paid in full.
It may feel bad, but they agreed to it.
Stand your ground. It's ok to be human.
