Hi L.,
Try making her nap time a bit later in the day (maybe mid-afternoon) and shorten that nap to no more than an hour. If she still doesn't seem tired, just tell her that this (whatever time you put her down) is "quiet" time. Leave the room and don't go back in no matter how much she screams (as long as all of her other needs are taken care of). She may be testing new boundaries, and if you cave in, she won't be getting the sleep she needs, and you will all pay the price. It will be hard, but she will figure out that she has nothing to do in there but sleep eventually. Or you could put her down when you usually do, and do the same thing. Because she is growing, her sleep/wake cycle appears to be changing, but it is important that she get back into a regular routine as soon as possible.
Is it possible that your daughter might need two shorter naps? Maybe put her down around 10:00 for an hour, then again at 2:00 or 3:00 for an hour.
It is also possible that she is one of those rare children who don't need a nap at all and prefer to get their sleep in one long stretch. If that is the case, put her to bed a little earlier and eventually she will sleep a little bit later. Children will get the sleep they need one way or another, but they do go through periods where they seem to resist it. If she is still acting tired around the time when she has been taking her nap, stick to your guns and put her in her crib for quiet time.
You are not being cruel or unreasonable by doing this. She is most likely beginning to figure out that maybe no doesn't mean no if she fights it hard enough. Make sure she knows that nap time will be nap time no matter how hard she screams. It is also possible that she hears the goings-on of her older brother and doesn't like missing out on the action.
If she is getting up earlier, even after not having a nap, that will change eventually, if you do take away the nap. The reason she is getting up earlier is because her sleep/wake cycle has been disrupted due to her not wanting to take her nap. There are so many hours a day she needs to be sleeping, so she won't go on like that forever. Either the nap goes back in, or she will start sleeping in later. Just be firm either way. If she is waking up at 5:15, don't go in there until it is closer to the time when she used to wake up. You will probably have to listen to some screaming but it will even itself out. And you will be glad you stuck to your guns.
I have great sleepers to this day because I went through things like this and decided that if I wasn't getting the sleep I needed (didn't want to get up at 4:30 or 5:00!), I wouldn't be equipped to handle all of their needs to the best of my ability during the day. If mom doesn't get enough sleep it's even worse than if they don't get enough sleep. They survived and gave up the fight eventually and rarely have getting-to-sleep issues to this day.
This is temporary, and it will pass. Many blessings to you and your family!