I recently tried to get very low light shots of my FIL and my 2 girls with a birthday cake lit with 4 candles. No tripod, no flash, auto mode and they were slightly blurry.
The tripod would help with camera shake, not with moving subjects. Since you had low light, no flash, and a f/3.5-f/5.6 lens, you would have needed a slow shutter speed for good exposure, but that same slow shutter speed might have caused blur from the moving subject. To minimize blur in this scenario, you would need to anticipate and press the shutter at the moment of peak action, when the subject is perfectly still. In addition, positioning yourself so the subject is moving straight towards the camera, rather than across the frame, minimizes motion blur.
So, what can I do to get good photos of the spectromagic parade, illuminations, fireworks, and rides like pirates and others?
For fireworks use a low ISO, small aperture (f/8, f/11 or f/16), set the focus to infinity, use a slow shutter speed (2 or 3 seconds, but you may need to mess around with this). USE A TRIPOD and either a remote shutter release or the timer. Zoom out far enough that you've got a lot of sky. For jpgs you might want to enable in-camera noise reduction. If you're including the castle in the frame, it's too easy to overexpose it.
For Spectromagic, a higher ISO may be necessary. That will cause image noise, but a noisy image is better than no image at all. The subjects will be moving, so if you want to reduce blur, you'd have to use a fast shutter speed, but doing so would necessitate a large aperture, which your lens is incapable of delivering. So, use the widest aperture you can (lowest f-stop) and play with the shutter speed until you get good exposure. Remember that because you'll be using your widest aperture, your depth of field will be shallow. Also remember that your aperture is variable, so if you set it to f/3.5 at 18mm, then zoom in to 135mm, your max aperture will change to f/5.6, so you may need to change your shutter speed or ISO accordingly. Shooting in aperture priority and using exposure compensation would make these adjustments easier on you. Positioning yourself so that most of the important subjects are on the same plane of focus will help. Find a spot before the parade starts and take practice shots of the crowd to find your settings. Also, you can reduce apparent motion blur by photographing the subject moving directly toward you rather than across the frame. Use continuous/burst mode to improve your chances of getting at least 1 good shot. Using a fast-writing memory card, rather than the cheap ones that offer large sizes will help. Crowds may not permit you to use a tripod, so use good hand-holding techniques: spread feet shoulder-width, tuck elbows in, support bottom of camera/lens with left hand, support the camera against your face while looking through the viewfinder, take in a breath...hold it...then squeeze and hold the shutter release button in one continuous motion--don't jab at it -- until the image has been recorded. You can further support yourself by leaning yourself or the camera against a post or something sturdy. A mini-tripod, or a beanbag, or a sock stuffed with rice can help steady a camera sitting atop a trash can.
Forget about trying to take pictures of the dark rides, like Pirates; just enjoy them. The characters are moving, you're moving, so they're going to be either blurry or underexposed. Using flash woud ruin the shot (you try to get a picture of Flounder swimming magically through the ocean onstage at the Little Mermaid show at Disney's Hollywood Studios, but, instead, you get a flash picture of a man dressed in black with a foam fish on his hand). Even with a wide-aperture prime lens, it's not worth it. But if you must take pictures on rides (without flash, please), then review what I seid above. Also, remember that you can further reduce the appearance of motion blur by zooming out. Motion is emphasized the more you zoom in. So, maybe that pirate audioanimatronic is smaller in the frame, but it will appear sharper than the close-up blurry ghost that kinda looks like a pirate.
I'm repeating this point, but you can greatly reduce motion blur by anticipating the perfect moment to take the shot. For instance, if you have to use a slow shutter speed, but you want a sharp image of someone jumping, you should take the shot at the split-second that they reach the apex of their jump. If you're a split-second too early, you'll get motion from them moving up, and if you're late, you'll get motion from the descending. This takes practice, but it's HUGE.
I took some photos of my DD4 at her swim lesson. I zoomed in on about 1/2 of them so that she was the focus of the photos instead of the rest of the people in the pool. Auto mode with flash. The photos were dark. However, when I zoomed back out, the photos were much brighter.
Your camera was metering for two different scenes, with different proportions and levels of shadows, highlights, and midtones. Additionally, your flash has greater effect on object nearer to it than your daughter who was farther away.
I'm probably one of those people who "shouldn't" have a DSLR because I just don't know how to use it correctly. I really want to learn more, but time is limited with taking care of my kids.
Most people in your shoes eventually give up on the DSLR, getting sick of lugging it around. Keeping this in mind, you might want to be careful about investing too much more money. You don't need expensive equipment to take great photographs. Fancy, expensive cameras help make it easier for photographers who already know what they're doing to do what they do well. Fancy, expensive cameras can intimidate and frustrate beginners, actually preventing them from improving.
How convenient that Mother's Day is coming up.
With the 50mm lens it's a fixed lens so wherever 50mm is, is where it will focus at. You have to get further back then you would with a zoom lens because of it being a fixed lens. Take your camera to the camera store and I am sure they will let you try it out. It really is a good lens. 
) but one other reason to choose the 50mm is that because it lets in a lot more light, it's easier for your camera to focus in low light, so you should have less times where the camera is hunting or even gives up entirely on getting focus.
I don't know what I was thinking. I swear, kids really do suck the knowledge out of you because I took not 1, but 2 photography courses in college. Apparently, that was too long ago. I won't confuse it now.
) I really like The Digital Photography Book by Scott Kelby. He gives you specific 'recipes' to get the type of photo you want to take. He also shows Canon and Nikon and explains a little about the differences in each camera to get the shot. So that's good and will help you get a little more familiar with your camera settings as a side benefit.
