Firstly: 

The hadeeth mentioned was narrated by at-Tirmidhi (3527) via Abu’l-Ward from al-Lajlaaj from Mu‘aadh ibn Jabal who said: The Prophet (blessings and peace of Allah be upon him) heard a man saying: O Allah, I ask You for patience. He said: “You have asked Allah for calamity; rather ask Him for well-being.” 

This is a da‘eef (weak) hadeeth. It was quoted by al-Albaani in ad-Da‘eefah (4520) and he said: There is some weakness in this isnaad. Abu’l-Ward is ibn Thumaamah ibn Hazn al-Qushayri, whom no one regarded as trustworthy. Al-Haafiz said: His reports may be accepted if there is corroborating evidence. End quote. 

Al-Qaari (may Allah have mercy on him) said: 

The argument here has to do with praying for patience before calamity strikes; however after calamity strikes, there is no reason not to ask for patience; rather it is mustahabb, because Allah, may He be exalted, says (interpretation of the meaning): “Our Lord! Pour forth on us patience” [al-Baqarah 2:250]. 

That is because asking for patience should only come after the calamity has befallen or the disaster has struck, or any situation in which a person needs to be patient. In that case it is prescribed for him to ask Allah for patience. Allah, may He be exalted, says (interpretation of the meaning):

“And when they advanced to meet Jaloot (Goliath) and his forces, they invoked: Our Lord! Pour forth on us patience and make us victorious over the disbelieving people.

So they routed them by Allah’s Leave”

[al-Baqarah 2:250-251]. 

And Allah, may He be exalted, said concerning the sorcerers of Pharaoh (interpretation of the meaning):

“They said: Verily, we are returning to our Lord.

And you take vengeance on us only because we believed in the Ayat (proofs, evidences, lessons, signs, etc.) of our Lord when they reached us! Our Lord! pour out on us patience, and cause us to die as Muslims”

[al-A‘raaf 7:125, 126]. 

But when one is in a state of well-being, it is appropriate to ask Allah to complete His blessing, and to grant well-being and protection. 

Secondly: 

There is nothing wrong, in sha Allah, with a person asking his Lord for patience, restricting that to calamity if it should happen, or if something should occur that requires patience. It is quite natural that man’s life should not be free of trials and tribulations in which he needs to be patient and to call upon Allah. Hence one of the supplications of the Prophet (blessings and peace of Allah be upon him) was: “O Allaah, by Your knowledge of the unseen and Your power over creation, keep me alive so long as You know that living is good for me and cause me to die when You know that death is better for me. O Allaah, cause me to fear You in secret and in public. I ask You to make me true in speech in times of pleasure and of anger. I ask You to make me moderate in time of wealth and of poverty. And I ask You for everlasting delight and joy that will never cease. I ask You to make me pleased with that which You have decreed and for an easy life after death. I ask You for the sweetness of looking upon Your face and a longing to meet You in a manner that does not entail a calamity that will bring about harm or a trial that will cause deviation. O Allaah, beautify us with the adornment of faith and make us among those who guide and are rightly guided.” 

Narrated by an-Nasaa‘i, 1305; Classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 1301. 

He asked Allah, may He be exalted, to bless him with contentment with that which He decreed. It is clear that what this means is a decree that one dislikes, otherwise everyone is pleased and content with that which he likes and which suits him. But this does not mean that this is a du‘aa’ that something disliked be decreed, just as the other du‘aa’ – in the same hadeeth – does not mean that one is asking for poverty or death. 

Thirdly: 

The fact that your son is quick to get angry is a matter concerning which it is appropriate to pray for patience. The one who is quick to get angry will react to the slightest annoyance and panic at any problem; undoubtedly he is the one who is most in need of praying for peace of mind, patience, calmness and a good attitude. Therefore this does not come under the heading of praying for calamity or seeking to hasten it; rather this is a prayer for the best remedy for him from the problem he is faced with. 

For more information please see the answer to question no. 120175 

And Allah knows best.