Ruth Rabbah 2:16 actually quotes the idea and source of rejecting three times (three mentions of rejecting in the story of Ruth), but seemingly it is not brought down l'halacha.
Very similar question, with quotation and translation of the source above:
Source for discouraging converts
I have frequently heard that a convert is treated identically to someone born Jewish, but this is not true. I know of one exception, a woman who converts to judaism is not allowed to marry a Kohen (Jewish man of the priestly line of descent). I would not be surprised if there are other differences in how converts are treated (but this may be the only one).
Shalom Cameron Carter.
(1) Regarding conversion, I would recommend you approach your rabbi. He will tell you the steps to take. Tell him you have Jewish roots. That will help tremendously!
(2) I recommend Maimonides. I think rationalism is the best form of Judaism and the most correct. It is also the most tolerant.