Although no proof was mentioned for such a question, but we must pay attention that a change of approach does not indicate a change of character and maybe the prophet did have an apparently different act regarding different issues depending on the time, place and situation, but we can not perceive any of these as a change of character. These different approaches had several other reasons that need to be mentioned separately.
This question can be explained in two parts from a more precise viewpoint:
First: Is it wrong to change the way of approaching and dealing with something and does it signify a change of character?
Second: Did bad and negative characteristics develop in the prophet after reaching power?
Regarding the first question one must say that every change of approach can not be considered a change of character and should not be perceived as wrong behavior, for example we will mention some changes which are not wrong according to religion and logic:
1- Sometimes a person is very close to a group of people and spends a good amount of his time for them, but later on because of changing his job his time is limited and therefore he cannot visit all of them the way he used to. In order to compensate, he decides to keep in touch through calling them. Such a change in behavior can not be considered a change of character and he should not be blamed. But if the same person does not greet his friends and denies their past friendship altogether after the improvement of his situation, then we can conclude that his character has undergone a negative change. We can look for a similar situation for parents when dealing with their first child after the second child is born.
2- If we respect someone because of him being religious and humble and then that person achieves a social position and changes to a proud and irreligious person, then the way we approach him will change as well, but this change of approach stems from the change of his character not ours!
3- If we are dealing with a disbeliever and an irreligious person that has fought against the Muslims, we will be harsh on him when going to battle with him, but if that same person decides to do some research on Islam, according to the command of Allah, we must provide him with utter security, and even if he is just our neighbor or our guest, Islamic teachings still dictate that we respect him.
There are many of these kinds of changes in one's behavior and approach which are approved of by our intellect and religion. In this light and in order to answer the second question, we must say that the behavior and conduct we see from the prophet is done in one of the abovementioned contexts or one similar to them and this is why the prophet's behavior and approach seems to have changed.
For example, it has been narrated that one day the prophet entered his house that was full of his guests. Since there was no more room in the house one of the prophet's companions by the name of Jarir sat outside of the house. After the prophet noticed he was there, he took off a piece of his own clothing and gave it to him and told him to spread and sit on it. When this companion felt such respect from the prophet, instead of sitting on the clothes, he kissed it and placed it on his face!
It was only possible for the prophet to do such an act for a limited number of his followers, but if his followers were to grow to thousands and all of them were eager to speak and associate with him, wouldn't continuing such an act dismantle his social and private life? (This change of behavior does not mean the prophet's character had changed, it was the situation that demanded him to do so for only a few of his companions.)
It is on these premises that Allah tells the believers: "Do not enter the Prophet's houses unless permission is granted you for a meal, without waiting for it to be readied. But enter when you are invited, and disperse when you have taken your meal, without settling down to chat. Indeed such conduct torments the Prophet, and he is ashamed of [asking [you] to leave]…"
Therefore when examining the two mentioned incidents, we cannot conclude that the prophet's character had changed and that he would not treat his followers the way he used to, but rather the situation had changed in a way that continuing such a behavior was not possible for him.
If we come across other examples of change in the prophet's behavior we must examine them carefully and discover the logic behind them, not to promptly conclude that his character has changed after coming to power.
Because you did not mention an example for your question we can not exactly examine what you had on mind, if you want you can send us the specific situations so that, with the help of Allah, we give you a convincing explanation for that specific situation.
But what is certain is that the prophet's character stayed the same during his life and he himself would criticize and oppose those who would undergo negative changes when achieving a certain social position. This is why he tells Imam Ali: "If I put my hands in the mouth of poisonous snake all the way till my elbow, it is easier for me than to make a request from those who have just reached a certain position [those who are arrogant and think they are on top of the world just because they have attained a position]." There are many other historic examples in this regard and we will mention two of them:
First: Imam Baqir narrates from the prophet that he said: "I will continue doing five things up until my death; Eating along with the servants on the ground and without a table cloth having an average means of transportation, milking goats with my own hands, wearing clothes made of wool and saying "Salaam" to children. And I do all of these so that others will follow in my footsteps.", and we find that he acted according to his promise.
Second: One of the prophet's followers came to him and after noticing the mark left by the mat on the prophet's body, he said: "I wish you would get yourself a better bed". The prophet responded: "What do I have to do with the world! The way I use this world is similar to the way a traveler gets some rest under a tree in a hot day of summer and then moves on immediately!"
Yes! People who view the whole world and what it consists of as nothing and view solely Allah as the everlasting, have a great character that will not undergo change or become proud (and act in a way other than what Allah has commanded) because of changes that take place in their earthly lives. We hope that we follow in the footsteps of our prophet.
Of course, as we mentioned above, all people including the prophet may, depending on the situation, show different behaviors and approaches during their lives that cannot be perceived as a change of character.
 Fat’h:29; Tawbah:73; etc.
 Al-Sha’iri, Taj al-Din, Jame’ al-Akhbar, pg. 84, Dar al-Radhiyy li al-Nashr, Qom, 1405 AH.
 Majlisi, Muhammad Baqir, Bihar al-Anwar, vol. 16, pg. 225, Al-Wafa’Institute, Beirut, 1404 AH.
 Hurr Ameli, Muhammad bin al-Hasan, Wasa’il al-Shia, vol. 9, pg. 440, hadith 12439, Aal al-Bayt Institute, Qom, 1409 AH. In this hadith, the phrase “من نم یکن ثم کان” has been used for those who were nothing and all of sudden became someone.
 Majlisi, Muhammad Baqir, Bihar al-Anwar, vol. 16, pg. 214, hadith 2.
 Majlisi, Muhammad Baqir, Bihar al-Anwar, vol. 16, pg. 249.