Is Istikhara responded in the form of a dream?
There is a question about a boy and a girl who wanted to marry. It was then, someone suggested them to do istikhara which resulted a few wrong types of dreams to the girl. Therefore her mother refused and stopped her from marrying the boy.
A popular myth about Istikhara...
Do Istikhara at night. Then go to sleep expecting a dream that will unfold the istikhara and if you do not see the dream then do Istikhara again the next day and wait again till you see a dream. Continue this till you see a dream. And when they do not see a dream they give up. This is a trap.
Istikhara was performed by the Prophet (peace and blessings of Allaah be upon him) when he wanted to decide on an issue which had two options. In other words istikhara has to be done when you want to reach a conclusion. That is what a part of the dua of istikhara is: O Allah make it easy.
The correct way of Istikhara...
The Prophet (ﷺ) used to teach us the way of doing Istikhara (Istikhara means to ask Allah to guide one to the right sort of action concerning any job or a deed), in all matters as he taught us the Surahs of the Qur'an. He said,
"If anyone of you thinks of doing any job he should offer a two rak`at prayer other than the compulsory ones and say (after the prayer):
Allaahumma inni astakheeruka bi ‘ilmika wa astaqdiruka bi qudratika wa as’aluka min fadlika, fa innaka taqdiru wa laa aqdir, wa ta’lamu wa laa a’lam, wa anta ‘allaam al-ghuyoob. Allaahumma fa in kunta ta’lamu haadha’l-amra (then the matter should be mentioned by name) khayran li fi ‘aajil amri wa aajilihi (or: fi deeni wa ma’aashi wa ‘aaqibati amri) faqdurhu li wa yassirhu li thumma baarik li fihi. Allaahumma wa in kunta ta’lamu annahu sharrun li fi deeni wa ma’aashi wa ‘aaqibati amri (or: fi ‘aajili amri wa aajilihi) fasrifni ‘anhu [wasrafhu ‘anni] waqdur li al-khayr haythu kaana thumma radini bihi
(O Allaah, I seek Your guidance [in making a choice] by virtue of Your knowledge, and I seek ability by virtue of Your power, and I ask You of Your great bounty. You have power, I have none. And You know, I know not. You are the Knower of hidden things. O Allaah, if in Your knowledge, this matter (then it should be mentioned by name) is good for me both in this world and in the Hereafter (or: in my religion, my livelihood and my affairs), then ordain it for me, make it easy for me, and bless it for me. And if in Your knowledge it is bad for me and for my religion, my livelihood and my affairs (or: for me both in this world and the next), then turn me away from it, [and turn it away from me], and ordain for me the good wherever it may be and make me pleased with it.”
Sahih Al-Bukhari – Book 21 Hadith 263
If performing that deed turns easy for you then Allah has made it easy, or else...
If that work for which you have done istikhara, becomes easy for you it means Allah has blessed it and if there are hurdles coming up and it becomes difficult then be sure that it is a response to your Dua because if you study the above Dua, it has a plead that, “if there is sharr (evil) for me in it then save me from it and take it away from me and keep me away for it.” Allah knew that it was not good for you so He saved you from it.
Dreams are not always from Allah
If you see a good dream then it is from Allah and bad dreams can be from Shaytan. Therefore in your case, everything was clear and was going good yet Shaytan might have showed the girl a bad dream in order to stop a Khayr. Thus she's confused. If Allah wanted to show the evil consequences of marrying each other in dream then He could have let you both see the same dream but it was not the case. Therefore, it could be a role of Shaytan to prevent a good marriage.
While deciding one should consider the ground reality too
One should not be too much depended on dreams. In cases, many at times people take up a good work with enthusiasm but on the way few hardships highlighted by shaytan cause it to stop. Therefore, when one has given commitment and it is in good faith then one should stick to it with a trust in Allah.
A bad dream may not always be a bad forecast as per your fear
In such a case one must discuss his bad dream with some senior who can interpret dreams according to shariah norms. It could be possible that the interpretation of a bad dream can be a good outcome as well. So it could be your own interpretation. Therefore, keep making Dua for the khayr and go ahead. I may even suggest the mother of the girl too that she should not be too pessimistic just because of a dream.
But if Shaytan has inserted an evil whisper as a forecast
It can happen that you have seen a bad dream after Istikhara but you go ahead as per the ground reality. Later on things do not go alright so you get those seeds of negative thoughts sprout with pessimism. Now it could be possible Shaytan may again incite you with the same thoughts if things go wrong in future.
Therefore, if the case is such that it can pop up in future, as it is firmly rooted in the heart of elders then it is better to drop the proposal because it could be possible that few negative traits in the spouse might grow bigger after the marital quarrel, reducing the affection between the spouse. Therefore, prevention is better than cure and both of you should consider all the plus and minus points and then decide whatever you want to.