Let me tell you what I have learned in this regard.

There are two things -- taqdeer and qismat. Qismat is the one that can be changed with hard work, prayers and the choice of path we choose to walk on. Let's suppose there are two paths, path A and path B. The choice of these paths is given in our hand. Whichever path we opt for, we'll have to face its respective consequences. These consequences are not always known to us beforehand. When we talk about 'qismat badalna', that is actually the choice of path that we make. Since Allah is the All-Knower, He knows the choices we will make throughout our lives: He knows the ultimate consequences of our decisions and it is that knowledge of the consequences that He has, that is written in our taqdeer.
Now coming to the second point... The acceptance of dua doesn't actually create problem, instead dua put things straight . It is how we pray that creates problems. If we make a dua humbly, bow in front of Allah and ask us to grant us something if it is beneficial for us and take away our desire for that thing if it is harmful to us; we either get that thing in a form we wanted it in, get something better or have our dua saved for the hereafter and get patience. What we usually do is insisting on getting the thing we desire of, we start reminding Allah of our good deeds and ask for that thing in exchange for our good deeds. Sometimes when we feel like we are not going to get that thing we tell Him how and how He has been unfair to us and how and how He didn't listen to our requests (naozubillah) but we don't bother to think that this could be for some wisdom of Allah. At such points we are granted we have asked for but later on we get to see the end-results of that zid. That's why some wise fellow has said 'kabhi kabhi Allah Ta'ala humain aik gul-dasta daina chahta hai aur hum sirf aik phool k liye zid laga kar baith jatay hain. Dua zaror maangain lekin bahut zid na karain'.

Hope you got your answer. I didn't quote any Aya'h aur Ahadeeth because whatever I have written here is reproducing what I have read at different places. Keeping exact Aya'h and Ahadeeth in mind is a difficult and error prone task.

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I don't give anyone a reason to HATE ME. They create their own drama out of PURE JEALOUSY...!!!