Assalamu alaikum wa rahmatulahi wa barakatuh,
In your case, there are a few ways that you can consider in managing the behavior of your 3-year-old. It is not unusual for three years old to behave in this seemingly angry and impatient way. Firstly, we have to understand that there could be any number of reasons why she is behaving in this way and if we address the root cause first are more likely to be successful in overcoming this difficulty. Commonly, three-year-olds behave like this because they either fell that they are not being heard, they are trying to get your attention, or they are jealous of other siblings. In all these cases there are various things you can do to build positivity in them.
Ensure you set aside each day to spend time with your 2 daughters individually, giving them each a bit of one to one time with you so they can each have a turn at being the center of your attention. This will make them feel loved and cared for a less in need to have angry outburst to get your attention.
In addition to having one to one time, also ensure that you make time for activities that involve you all together. This will support the building of relations between the 2 sisters as well as with you. This way you are less likely to encounter severe sibling rivalry. In your case, you also say that your five-year-old gets on with whatever you do, but the three-year-old does not so be careful that the way you communicate with them does not put across a message that might imply that you are favoring one over the other.
Instead, commend your five year old when she does something good and let the three-year-old see this and perhaps feel like she could get your attention and praise if you behaved in the same way, but additionally, when your three-year-old does listen to you and does as you say, even if it is something relatively small, make sure to give her a bit of praise for that too so that she will desire to listen to you more to get you positive attention.
Likewise, in her angry moments, begin by coming down to her level and gently asking her what the problem is and see if you can come up with a resolution. If she does not respond to this then try to avoid giving her attention, preferring to ignore it where possible. This way, she will learn that the only way she makes you happy and gets your attention is when she does something that you like.
May Allah reward your intentions to raise your daughters in the best way. May He give you the strength and patience to endure the challenges that come with parenthood. May your daughters grow up to be pious, upstanding pillars of the community who are the coolness of your eyes.