If her husband prevents her from visiting her parents, will she be rewarded for her intention?
Question

Is it more important for the son to be good to/respect and look after the parents than daughters or are sons and daughters equal in their responsibility? If a daughter is married and her husband does not allow her to see them unless it suits him, she is unable to serve her mother even though she wants to, does she get rewarded for her desire even though she is unable to do so, even though her husband knows the rquirement and behaves well with his own mother?.
Praise be to Allah.Firstly: 
Honouring one’s parents is a duty on all children, male and female, and there is no difference between them in this regard, because of the general meaning of the evidence which enjoins honouring one’s parents and treating them well, such as the verses in which Allah says (interpretation of the meaning): 
“And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour.
24. And lower unto them the wing of submission and humility through mercy, and say: ‘My Lord! Bestow on them Your Mercy as they did bring me up when I was young’” [al-Isra’ 17:23, 24] 
“Worship Allah and join none with Him (in worship); and do good to parents…” [al-Nisa’ 4:36]
Al-Bukhaari (527) and Muslim narrated that ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) said: I asked the Prophet (peace and blessings of Allah be upon him) Which deed is best? He said: “Prayer offered on time.” I said: Then what? He said: “Honouring one’s parents.” I said: Then what? He said: “Jihad for the sake of Allah.” 
Al-Bukhaari (5971) and Muslim (2548) narrated that Abu Hurayrah (may Allah be pleased with him) said: A man came to the Messenger of Allah (peace and blessings of Allah be upon him) and said: Which of the people is most deserving of my good companionship? He said: “Your mother.” He said: Then who? He said: “Then your mother.” He said: Then who? He said: “Then your mother.” He said: Then who? He said: “Then your father.” 
This evidence and other texts are general in meaning and enjoin children, whether male or female, to honour their parents, but some kinds of honouring the parents may be easier for males than females, such as visiting the parents regularly, because a woman’s husband may prevent her from visiting her parents or visiting them very often, as mentioned in your question. 
Secondly: 
If the husband prevents his wife from visiting her parents, does she have to obey him? There is a difference of opinion among the fuqaha’ concerning that. The Hanafis and Maalikis are of the view that he does not have the right to prevent her from visiting her parents. 
The Shaafa’is and Hanbalis are of the view that he does have the right to prevent her, and she is obliged to obey him, so she should not go out to visit them except with his permission. But he does not have the right to prevent her from speaking to them or to prevent them from visiting her, unless he fears that some harm may result from their visit, in which case he may prevent them so as to ward off harm. This has been discussed in the answer to question no. 87834. 
Thirdly: 
If the wife wants to visit her parents and serve her mother, but she cannot do that because of her husband, then she will be rewarded for this desire and good intention. The saheeh Sunnah indicates that the one who wants to do a good deed and is eager to do it will be rewarded like one who did it, if he is unable to do it. 
Al-Bukhaari (4423) narrated from Anas ibn Malik (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) came back from the campaign to Tabook and when he drew close to Madeenah he said: “In Madeenah there are people who, whenever you travelled any distance or crossed any valley, were with you.” They said: O Messenger of Allah, even though they are in Madeenah. He said: “Even though they are in Madeenah, because they were kept there by excuses.”  
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said in his commentary on al-Bukhaari: This indicates that a man may attain by means of his intention that which the one who does the deed may attain, if he is prevented from acting by some excuse. End quote. 
Al-Tirmidhi (2325) and Ibn Majaah (4228) narrated from Abu Kabshah al-Anmaari that he heard the Messenger of Allah (peace and blessings of Allah be upon him) say: “Four people are making the most of this world:
a man to whom Allah gives wealth and knowledge, so he fears his Lord with regard to the way in which he disposes of his wealth, and he uses it to uphold ties of kinship and he realizes that Allah has rights over it. This man occupies the highest status. And a man to whom Allah has given knowledge but did not give him wealth, so he is sincere in his intention when he says, ‘If I had wealth I would have done the same as So and so is doing.’ So he will rewarded according to his intention and the reward of both of them is the same…” 
Classed as saheeh by al-Albani in Saheeh al-Tirmidhi. 
The husband should treat his wife kindly and help her to honour her parents. This is good treatment which Allah has enjoined, as He says (interpretation of the meaning): “and live with them honourably” [al-Nisa’ 4:19]. 
May Allah help us all to do that which He loves and which pleases Him. 
And Allah knows best.