Three year old girls are hard work - I call mine a threenager! Having been there twice it does sound like she is full on but showing normal 3yo behaviours.

I found with DD2 that I need to set very firm boundaries eg. if she has a tantrum at swimming and refuses to do what is asked or behaves in a way that is dangerous then we leave. If it is more of an emotional meltdown then I need to remove her from the situation, sit somewhere quiet and just have some cuddle time.

It's not that she is spoilt but she will be having lots of emotions and doesn't have the maturity or understanding of how to deal with them. She will also probably behave differently for different people eg DD2 does things for DP that she won't do for me and vice versa. I find DD2 is also dreaming a lot and has trouble differentiating dreams from reality, she just doesn't understand yet. The leg thing might be a fabrication but could also be growing pains - heatpacks are a good idea for that.

I found with DD1 that she did get a lot better as she approached 4 and I notice that DD2 is already having fewer meltdowns at 3.5 than she did at 3 so it does get better. In the meantime set the non-negotiable boundaries (safety etc) and try to help her by guiding her emotions until she can do it herself.