Shabbat 141 - July 25, 4 Av

In what cases can one move things that are muktze indirectly? When one comes out of a river on Shabbat, one needs to worry about carrying water that is on one's body and therefore should dry off before walking. How can one clean off dirt off one's foot on Shabbat? How can one clean dirt off one's clothing? Can one scrape dirt off a shoe? Can one remove a shoe from the shoe frame? Why can't a child go out with shoes that are too big or a woman wearing shoes she has never worn before? Can one carry a child if the child is carrying a rock in its hand? The mishna discusses cases where an item can be considered secondary to another and therefore will be able to be carried together with it and is not considered muktze. The gemara brings up cases regarding carrying from a public to private domain a child with a purse around its neck. The conclusion there is different from the mishna as there we obligate one for carrying the purse. Why the difference?