Will the wife in Paradise be obliged to obey her husband and live with his other wives?

Firstly: 

The life of the Hereafter cannot be compared to the life of this world, because they are completely different. al-Bukhaari (3244) and Muslim (2824) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Allah, may He be glorified and exalted, said: I have prepared for My righteous slaves that which no eye has seen, no ear has heard, nor has it ever crossed the mind of man.” Recite if you wish: “No person knows what is kept hidden for them of joy as a reward for what they used to do” [al-Sajdah 32:17]. 

The people of Paradise will not enter Paradise until they are purified and cleansed, and Allah removes all resentment from their hearts, as He, may He be exalted, says (interpretation of the meaning): “And We shall remove whatever is in their hearts of resentment, (So they will be like) brothers facing each other on thrones” [al-Hijr 15:47]. 

Al-Bukhaari (6535) narrated that Abu Sa‘eed al-Khudri said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The believers will be saved from the Fire and will be detained on a bridge between Paradise and Hell, where they will settle scores with one another concerning the wrongs that were done between them in this world until, when they are purified and cleansed, permission will be given to them to enter Paradise.” 

Then when they have entered Paradise, there will no longer be any of the troubles and annoyances of the life of this world. 

When the believer enters Paradise, he will have whatever Allah wills of al-hoor al-‘iyn, so there is no sense in wondering about jealousy of wives, or defiant disobedience on the part of the wife, or mistreatment on the part of the husband. Muslim (2836) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Whoever enters Paradise will enjoy bliss and will not be miserable.” 

Muslim also narrated (2838) from Abu Moosa al-Ash‘ari (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “In Paradise the believer will have a tent made from a single hollowed-out pearl, sixty miles high (or wide), in which the believer will have wives and he will go around among them and they will not see one another.” 

Look at what the Prophet (blessings and peace of Allah be upon him) said: “… and they will not see one another”, even though they will be in a single tent. That is in order to increase the blessing and avoid the causes of jealousy. 

So there will be no room for annoyances and problems, and there will be no causes that would lead to that which they lead in this world of jealousy and so on. 

Paradise is the abode of blessings and reward, not the abode of obligations and tests. There is no obligation in Paradise to obey anyone, or to carry out any duties; rather what there is in it is blessing that will never end, and its people will be in a state of joy morning and evening. 

Allah, may He be exalted, will bless the people of Paradise with boys who will serve them , so no one among the people of Paradise will require the service of his wife or his son or anyone else; there will not be any of those mahaam ma ‘eeshiyyah that require service, such as making dough and bread, and so on. 

When the people of Paradise enter Paradise, there will be no exhaustion or weariness, no worry or grief; rather it will be everlasting delight. We ask Allah, may He be exalted, to make us among its people. 

For more information, please see the answer to question no. 25843

And Allah knows best.