Can I give you my (probably unwanted and unpopular) opinion?
I think it's soooooo important to have a backbone and to stick to your policies. BUT, I also think it's good to be flexible. If a parent of mine didn't give their two week notice for vacation, I would just remind them of my policy and tell them (in the future) to PLEASE inform me in advance.
If someone pays late (rarely happens) I tell them "no worries" and have never charged a late fee. 95% of my parents don't take advantage - thank goodness.
I feel in this economy it is important to give a bit. Most of my new clients are referrals and that is because my parents are happy. I would just hate to see you (or anyone on here) lose a wonderful family due to something that isn't a huge deal.
Please don't throw cyber-tomatoes at me.