While I can see your point OP, in reality they already gave this one-day-a-week sitter a weekly gig and it would be unfair of them to simply fire her because you need the day too.
Even if they did do this, it would only be a matter of time before they screwed you over too.
Your boss sounds quite decent to me to be so loyal to her employee. Be grateful that she is, not all are.
I wouldn't ask her again. You already discussed this with her so she knows how you feel. Bringing it up again will not change anything.
Either a). Look for a new position with more hours or b). Pick up some babysitting on your days off.
Either way, good luck.
