So what type of set up/settings are you supposed to use for movement?
OK, can clarify by saying the following:-
1) The received wisdom is that AI Servo works well to moving subjects that are coming towards/going away from you on a (reasonably) predictable path ~ think racing cars on a track, a footballer running towards the goal a gaol kick attempt, aircraft coming in to land, birds in flight. Even these subjects can be difficult to capture exactly in focus frame to frame 100% of the time because as stated before AI Servo will allow the shutter to fire whether subject is still in focus or not!!!
2) A 2 year old running around especially in close proximity to you the photographer will not be so predictable ~ I did suggest trying a longer lens than 50mm & being further back form the subject and getting her to play with her mum i.e. try to get some predictablity in the direction she will run?
3) Portraiture is not about movement unless it is intended for artistic effect ~ where you (typically) require absolute sharpness of the facial features e.g. the eyes then you need stabilty and the subject to pose. And one shot focusing rules
4) Using a flash will allow you to freeze the moment/movement in time ~ think of the Paparazzi with their flashies blitzing away when their "prey" is rushing by them at a rate of knots
5) Carefull choice of aperture to increase the DoF can help but is not a guarantee of ensuring the eyes are still in critical focus
6) Having said all the above technology can help in that the higher grade & spec cameras have improved control of the AF system. By that I mean my old 350D had very poor AI Servo but my 40D is way improved! Looking say the 7D it has what I undestand are called hidden focus expansion points that surround the central AF point this aids keeping the subject in focus between shots when using high frame rates shooting and AI Servo.......the 1D MkIV being the top end Pro body takes that to a level my wallet can dream about!
I do hope that helps you understand that limitations of the camera, the user, the lens choice will impact on how well your expectations of the final image meet the actual final image.
The fact that you are struggling to get what you perceive as "good" images does not mean you are a poor photographer......you are learning and will continue to learn until the day you decide to give up.
Keeping taking pictures, learn the capabilities of of the kit you have now and its limitations and when you can clearly undestand and are sure that it is indeed the kit holding you back then is time to say "what do I need to take it to the next level & can I afford it...."