I have read and heard in certain places that among certain Orthodox groups, if one converts with Chabad-Lubavitch that their conversion will not be valid, if someone were to convert with Chabad and then decide later to join the Breslov movement, or Satmar. Would that person have to undergo conversion once more? I want to convert to Judaism and am currently at a Chabad shule but I have been becoming more interested in the Breslov movement, and there is no Breslov shule in my country, would I have to undergo conversion once more to be accepted fully in other Orthodox groups if I had converted with Chabad already?
In Breslov specifically we are careful to adhere to the Rebbe's words and avoid any unnecessary stringencies. As such, a conversion by a shomer Shabbos beis din that involved bris mila, mikvah, and sincere and total kabalos mitzvos would generally be seen as valid to most Breslov communities and individuals.
All that said, to the best of my knowledge Chabad does not perform conversions.
I think that the answer to this question is "it depends." If the Chabad-trained conversion candidate does not espouse "Meshichist" doctrine -- the advocacy that the deceased Lubavitcher Rebbe is/will be the Messiah, in contradiction to the Rambam's position that a deceased person cannot come back to be the Messiah -- then I doubt there will be any issue in most communities. But if the candidate willingly takes the position that the Rebbe is/will be the Messiah, the proability of approval is less likely.
This issue came up in Israel in 2007 when a Chabad-educated conversion candidate applied to a senior beit din counsel to have his conversion authorized. During his interview with the three rabbis he espoused meshichist views. The decision was elevated to four senior rabbis, two Modern Orthodox and two Haredi rabbis. The Haredi rabbis were inclined to approve the conversion, while the Modern Orthodox pair were not, ruling that an exponent of messianist beliefs cannot be converted to Orthodox Judaism. In the end, the Conversion Authority in Israel adopted the position of the opposing rabbis and stated: "They [messianic Chabad Hassidim] attribute to him supernatural powers years after he passed away. That is not Judaism. It's something else."
One could also infer that Chabad conversions might be rejected, if the convert was a meshichist, from statements by such individual gedolim as Rav Aharon Feldman, shlita, Rosh HaYeshiva of Ner Israel Yeshiva and a member of the Council of Sages, and Rav Shlomo Eliyahu Miller, chairman of the beis din of Toronto. Rav Feldman, in a public letter, and Rav Miller, in the April 2008 issue of Mishpacha Magazine, both said that they would not recognize the decisions of a Meshichist rabbi.
I really feel for what you are going through right now. It is unfortunate but there are politics that surround even this issue at times. My suggestion is to work with your sponsoring rav and find the least controversial beis din as possible. I would suggest looking into what ou, young israel, and aish have to offer as far as the conversion process. After your gerus what hashkafah and community to chose to be a part of is up to you and isn't relevant to the ritual of the conversion process. There are three main components for conversion and only three that matter... 1.acceptance of all of the mitzvas and fundamental beliefs (13 principles of faith) 2. mikvah and 3. bris milah (or hatfas hadam habris). May G-d almighty bless you in your journey.
[Speculation:] I do not believe you would have a problem with Breslov, since Chabad and Breslov are pretty close.
Satmar though, I don't know. There is unfortunately animosity there.
There is also animosity between Chabad and followers of Rav Shach.
Aside from any Halachic issues that may or may not exist (and that depends on whom you ask - if you ask followers of Rav Shach or Satmar they might tell you it is Halachic; if you ask followers of Chabad they might tell you it's not) there are also, unfortunately, politics at play dating back to a controversy between Chabad and Rav Shach in the knesset in 1988 relating to many issues, including peace and giving away land). Unfortunately, political and ideological disagreements aren't any easier to overcome than religious disagreements.
Yehi Ratzon (May it be G-'d will) that there should be peace between Jews even when we don't agree.