Marriage with my moms' mom's sister's daughter's daughter.

There are two aspects through which we have to see and examine this type of relationships. First is the cultural ethics as per which in many Hindu tribes and societies marriage in close relation is considered unethical. At the same time in some Hindu tribes it is permitted also. So if in your community it is accepted by and large then there is no confusion and one can go ahead with this. Another aspect is legal validity and as per the Special Marriage Act 1954, in Hindus, marriage in close relations is illegal. It is also mentioned in the law that relationship extending to three generations (considering the present generation as first generation) in mother side and five generations in father side, known as Sapinda relationships, are restricted for the Hindu marriages in the eyes of law in our country. The law also stipulates that if this type of relationship is accepted and allowed in the community then law does not come in way of this.

In your case it is moms' mom's sister's daughter's daughter which is clearly away from the three generation mother side straight linkage known as sapinda relationship and in view of that you can go ahead with that relationship.

There is no Astrology involved in the above answer and if you have belief and faith in Astrology then you have to present the horoscope of both the persons to a reputed Astrologer and seek his advice.

Here the prime consideration is the tradition and practice in your family and community.
Generally this kind of relationship is not encouraged and as far as possible, avoided. The legal status also prohibits this kind of marriage because there is common ancestry within 3 generations. As most communities in Hindu religion are to perform Pinda /Tharpan( ceremonies to ancestors) upto three generations minimum on both maternal and paternal sides, this kind of relationship may come under Sapinda relationship. Hence it is avoided.

However some communities follow this strictly only on the male lineage. Hence you may have to conform to the family and community traditions and practice.

In case the relationship is allowed and permitted in the family and community tradition and socially accepted, you may proceed for marriage.

In that case do not bother about astrology. Ignore it. Consider mutual love and affection and family support and go ahead.

Legally you will not have any problem as the relationship is not immediate it is more than 3 generations of blood relation.
But if you go by the relations, your grand mother's sister's granddaughter. You both will be a brother to her. She will be a sister to you. This is as for the relations we follow in the Telugu states. A girl can marry her grandmother's (Mother's Mother) sister's son's daughter. But a boy can't marry his grandmother's (Mother's Mother) sister's daughter's daughter. But these customs differ. What is the tradition in your family? You have to discuss with your elders and take a decision.
If both of you decide and want to go ahead, you can go ahead as the relationship is very distinct. I know some people who married like this and they are happy. No problems are being faced by them. Elders may not accept. You have to convince them.

You have disclosed your relationship with the girl and by that relationship she is your sister. Though this is the case of a sapinda relationship but for that you need not think so seriously and this can be settled amicably with the advice of the lawyer.
However, this has to be seen in two different angles prior to finalisation of this relationship-
1) You need to understand the girl very closely in relation to her attitude, her sensitivity towards the problem solving issues, her patience in the crucial hours and after all how far she would be cooperative with you in solving the different issues of the life.
2) Ensure that she is mentally stable while taking decisions.
3) Some problems may arise which may be termed as the genetic issue where due to variation of Rh Factor of the couples may end up the abortion of the wife. Hence it would be utmost important to get the blood tested to confirm the absence of such an abnormality.
If everything thing goes in favour, there is no point to delay this marriage.

Marriage is a decision that connects two people with two families, so it is prudent to include members of the household in its decision. Marriage is an important subject included in the law and all the provisions relating to marriage are given in the Hindu Marriage Act. Sapind relationship is more important under this act. After marriage, it is a necessary condition not to be spontaneous with each other. According to Hindu scriptures, the Sapind relationship is of utmost importance in 3 things - marriage, succession, and birth and death. Marriage is prohibited in the same family for three generations from the mother's side and five generations from the father's side - within the criteria laid down for it.