here is a synopsis for you of what everyone has told you-
you are only entitled to a child swap "ticket" if your child is shorter than the required height for the ride. some CMs at the entrances however, will sometimes feel bad for you and give you one anyway if you look pathetic enough/cry hard enough/beg hard enough
first time going on the ride- the parent may go either stand by line or fast pass line if you have a fast pass, just like anyone else in the park
second time going on the ride- the other parent (and up to three others although you don't have three others) go to the fastpass line and show that child swap "ticket" and go right on the ride. yes, some fast pass lines have a little wait, but it is usually almost nothing- basically you walk on
you seem worried about going a second time, the fast pass line is usually quick, don't worry.
you seem worried about your child being impatient, disney usually has some type of entertainment or play area near most rides. utilize them. for example, have dad go on splash mountain while child plays in the really cool play area there, then vica versa. your daughter will be entertained while both of you ride. when you pick up the child swap ticket, ask the CM for closest entertainment or play area. they'll know
while i understand this is your first trip to WDW, you may want to limit the number of rides you do without your little one. pick the biggies- skip those not that important to you
but don't push your kid to do things she doesn't want to. i have seen from personal experience, once they are afraid on a ride you told them they wouldn't be- all trust is lost, and getting them on ANYTHING else, even small world is darn near impossible.
but yes, despite your prior post, there IS a major advantage of child swap. they are fast passes for four. you just may not qualify for many of them