Some wild and interesting thoughts occurred to me last week, and I hope you will indulge me for a few moments. I do not have a source for any of my conclusions, but the basis is information you will recognize, and the implications will be quite intriguing.
When the Torah describes Dina's birth, the commentaries say something rather interesting. Originally, Leah was actually pregnant with Yosef. However, when Leah realized she was carrying a boy, she knew the ramification of this would be that Rochel would end up with less boys than the maidservants. This embarrasment could not be tolerated, so she davened that the child be switched to a girl. Thus Dina was born. (See the Da'as Zekenim.)
Immediately we see a connection between Yosef and Dina.
The Rabbenu Bachai says that Yosef was in fact born seven months after Dina, so they also were extremely close in age.
What is interesting to note is that at first glance it would seem that the power of Moshiach ben Dovid was rooted in Leah, and the power of Moshiach ben Yosef was rooted in Rochel. This, however, seems to not be the case. Rather, it seems that Leah had both potentials within her, and Rochel only birthed Yosef because of Leah's prayer.
The truth is, however, that we could look at it somewhat differently. Really, Rochel had the potential for both Moshiach ben Dovid and Moshiach ben Yosef within her, however, her sacrifice on behalf of Leah that she not be embarrassed when Yaakov ended up marrying her resulted in Leah supplanting her on both accounts. Leah's prayer on Rochel's behalf - that Rochel not be embarrassed - resulted in Rochel getting back the potential of Moshiach ben Yosef.
Still, it seems that Dina, while she was not a boy, still retained something of the spiritual power of Yosef. How do I know this? Because we find that the commentaries explain the following problem. Why did the entire event of Dina being raped by Shechem occur? One of the explanations given is that Yaakov was punished for witholding Dina from marrying Esav. She could have returned him to the side of good, and Yaakov prevented that from happening. Since she did not willingly wed a circumcised man, she was forcibly brought into a union with an uncircumcised animal - Shechem.
The obvious question is, Why should Dina be able to get Esav back on the Derech? How could Yaakov have known she possessed this capability?
The answer is that Yaakov knew that Dina possessed the same spiritual power as Yosef. Just as he knew that Yosef was the counter-balance for Esav, and therefore returned home as soon as Yosef was born, so too, Yaakov knew that Dina had the same spiritual balance for Esav! She would certainly have been able to get him back on the correct path.
Now the question is, Why would Yaakov indeed prevent Esav from getting back with the program? This question needs further thought, but a few different ideas come to mind. One is that Yaakov had bought the bechora and had also received the brachos of Esav. These brachos were the ones designated for the job of Moshiach ben Yosef that Esav originally had been supposed to perform. These very brachos would eventually be given to Yosef. It could be that Yaakov felt that Esav had lost his right to be in the program and first he, and then subsequently Yosef, had taken his place. It seems that this was not a proper calculation, as Dina ended up being forced into this horrible situation as a result.
There is more, however, because we find that who does Yosef end up marrying in Mitzrayim? Her name was Osnas, but who was she? There is a tradition that she was actually the product of the union between Dina and Shechem! Thus, Yaakov wanted to exclude Esav and replace him with Yosef. The result was Dina being raped and producing Yosef's future wife who would give him Efraim and Menashe! These two represented the special status Yosef had as bechor. Here too, Yosef had been given the first-born status taken from Esav by Yaakov.
There's still more. When Yaakov gives Yosef the bracha and tells him he will get a double portion, the language he uses is "Shechem echad" - you get another 'shoulder' over your brothers. The commentaries explain that there is a double meaning here. Besides for it referring to the double portion of two shevatim coming from him, it also refers to the actual city of Shechem, which Yosef would be buried in. But what does the city of Shechem have to do with Yosef? And why does he use this strange term to refer to Yosef's double portion?
The answer is plain to see. Because of Yaakov's desire to keep Yosef as Moshiach ben Yosef, Shechem raped Dina. This led to Shimon and Levi killing all the inhabitants of the city and it being conquered for the people of Israel. This city existed as part of what Yaakov bequethed to his children because of his commitment to Yosef. Shechem was the source of Yosef's special status and his double portion in the Jewish people both in concept and in physical reality!
It is also significant that when Yaakov refers to the conquest of Shechem, he refers to it as the place he gained through his sword and his bow. The commentaries say that this is reference to Yaakov's spiritual powers. Rav Aryeh Kaplan points out (in a different context) that the bow represents the power of Moshiach ben Yosef - shemiras habris - keeping the sanctity of the sexual organ. The commentaries explain that the sword is reference to the concept of tefillah and Torah. Thus we see that the two 'weapons' that Yaakov used to conquer Shechem corresponded to the job of Moshiach ben Yosef (the bow - shemiras habris) and Moshiach ben Dovid (the sword - prayer). This could hint to the fact that the entire reason for the event that transpired in Shechem was because Yaakov wanted to retain these two powers exclusively for his children, and specifically, Yosef.
One final addendum is something I saw in the Jewish Encyclopedia in an article on Shechem. There it mentions that Shechem was the city where Rechavam was appointed king, and later where Yeravam was also appointed. Yeravam actually made Shechem into the capitol of his kingdom. The significance is that Yeravam was literally inches away from being Moshiach ben Yosef, and Rechavam would have been Moshiach ben Dovid. The fact that they were both appointed in Shechem points to the fact that they recognized that their power was rooted in the city, and specifically Yeravam, as Moshiach ben Yosef, made it the center of his kingdom, for he recognized that his potential for greatness was there.