When I mixed up and forgot to pay a new rate at our daycare, they nicely informed me, in writing, what was owed and when. Put everything in writing and keep a copy. I didn't have the option to pay my vacation week whenever I felt like it. If I was taking DD out for the week, I still owed them the week on schedule. They still had bills to pay. We paid upfront before we left (my household DH and I split the costs so we both submitted a check before an upcoming vacation.) Failure to pay on time was a fine. Failure to pay on time more than once or twice could be grounds for removal from the center. Do not let HER tell YOU when YOU will get paid when she's already late.
I think you need to remind her the rules (print out a copy of the agreement or parent handbook) and say (in writing) that you will need her to pay her back vacation time by x date and start bringing her child either fed or during breakfast time. This is her notice. Then if she continues, inform her in writing that failure to abide by the rules (state rules broken) has forced you to ask her to take her child to a childcare provider that better suits her needs. Give her whatever notice is required in your contract.
I overheard part of a conversation between the director of my old daycare and a parent stating that since they had been there longer than the probationary period, whether or not the child was still in their center (parents were moving the child) they owed the center full payment for 2 weeks as per the contract. (We were supposed to give the center 2 weeks' notice.) I never got sick days for my kid and only earned 1 free week after 1 full year of attendance. You have a VERY nice policy!
You might feel for the kid and you might like the kid, but it is frankly a business arrangement and the mother is not abiding by the contract. You have other clients that can follow the rules and their kids deserve to go play at the scheduled time. If she can't feed her kid before she arrives, that's her schedule problem, not yours. I got my DD up at 6 and had her in the daycare by 8 with a 45 minute commute. Kiddo was always fed before arrival.
As for your schedule and fees - places vary. The costs I incurred are very different than back home because ALL costs are different. Your fees might be right in line with your area. If you didn't present the schedule to prospective clients upfront, then you should, but it sounds like she knows the schedule and isn't abiding by it. If she doesn't, then inform her or remind her what the schedule is. I wouldn't charge someone $1 minute fee for being "late" to drop off, but I would charge $1 minute for late pickup. We had to pay $1/minute directly to the person who stayed however long for us, unless there were extenuating circumstances. Most providers have this rule. I picked up a friend's kid yesterday because his parents could not get there on time and they did not want to be in the preschool's bad graces (or pay a fine).