I only read a few of the responses, so if I am repeating...sorry. But, I do have to say that your concerns say a lot about you. You seem to care about this little girl and that is the most important thing. As the child of divorce (and having dealt with two step-mothers over the years), I think it is important for all parents to be involved with the raising of the child. If you truly love your BF and you are prepared to deal with the ex for the rest of your life, there are a lot of things you can do.
Yes, some of the things you mention are normal for a 4 y/o, but if she is acting differently and is able to go dry through the night at her dad's house, then it probably is laziness.
At 4, she is old enough to learn reasoning and this is something you can begin to teach her. With the shoes, after she calmed down you could talk with her (notice I say with) and ask her if she remembers that the last time she wore "dress-up shoes" she fell or got a blister or whatever, teach her...it's the perfect opportunity. The next time you get ready to head out, mention something like "remember the last time you wore those shoes, you got a blister and it really hurt and made for a not so fun time." Give her the power, and give her a chance to be in control in a positive way.
I don't agree with the whole, this is none of your business. Maybe it's not your place now, but if you marry him, it will be your business. As you will want to raise this child the same as you would your biological children. Remember, you are in a very sticky spot. Regardless of whether the ex is a good mom, you will likely always be the bad guy. But if you are looking long term with your BF, it is important that you develop a trusting relationship with his children. I could write for days about the importance of step-parents being involved with the step-children. You may not be married to her daddy now, but you could be in the future and it is important that the two of you show a united front and take raising your children as a team effort. I