Your friend is taking you for granted, but you have let her.
She is being very cheeky, saving themselves money and dumping unpaid childcare on you. I imagine there must be times when having her daughter around might not be convenient for you, when you wanted just to attend to your own children, and as for getting you to look after her baby for a whole day, well that's a real burden to you, and I am surprised you agreed to do it considering it was your treasured annual leave/child free day, and I do think you should take responsibility for sabotaging your own day off, you could have said "no, I can't, got things to do" or whatever.
You need to insert some boundaries with your friend, stop agreeing to have her daughter every week, unless it's for an occasional 'play date' at your discretion (since your daughters are friends afterall), and DO NOT under any circumstances agree to look after her baby again as that is a full-on nanny task which prevents you from getting on with anything else you want to do.
How you convey this to your friend without causing a rift may be tricky, but I would suggest you ask her for a private/child-free chat in person one day, and then explain how you are unhappy with the current arrangement, as it interferes with your plans occasionally and restricts any impromptue family plans, and that you think she is using you as an unpaid childminder which makes you feel like a mug, especially as you pay exhorbitant (I presume?) fees for your own childcare - and that you cannot understand why did not persue the childcare you recommended before just to save herself some money - yes, childcare is expensive, but cost is worth it when you know your children are safe and you are not constantly imposing on other people to look after them instead. Hopefully your friend will value your friendship too much to get snotty with you, and should understand the pressure she has put you under but if not then at least you have made your point and she won't bother you again for childcare.