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

Praise be to Allah.

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 better 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.