You pose a complicated question and a precise answer might depend on details you have not shared in your post. For the most reliable response I would consult a rabbi you trust can hear all of your concerns. I can offer a more general response.
On one hand you want to be sure to do no harm to your children. The best path, then, is to be transparent to them. To let them know the process you went through on your path of conversion. Once they are armed with that information, they can decide when and how they need to share that with others.
On the other hand it is important to honor the decision you made to convert and the basic principles our tradition holds concerning that process.
Once one converts they are 100% Jewish for all purposes. The Talmud, B. Yevamot 22a, states categorically that “a convert is considered as a newborn child.” Once a Bet Din, a rabbinic court, has confirmed their status they are fully Jewish – without any further limitation or definition. This principle is reinforced when the Talmud, Baba Metzia 58b, states:
If one was a child of proselytes, one may not say to him/her, “Remember what your ancestors used to do.” If one was a proselyte who came to study the Torah, one may not say, “Look who's coming to study Torah which was given by the mouth of the Almighty! This one, who ate carrion and teref-keat, abominations and creeping things.”
This citation comes in the midst of a discussion of the Talmudic principle of ona'at devarim, wrongs committed by acts of speech. It is based on one of Leviticus 25:15, “You will not wrong one another.”
Sadly, the principle is often observed in the breach. Too often people ask when they shouldn't, and rabbinic leaders, who should know better, act as if they need to be universal gatekeepers for the Jewish people as a whole. Challenges to this or that conversion have become more common. The result is that no conversion – regardless of whether it was conducted by a Reform, Reconstructionist, Conservative or Orthodox Bet Din – can be considered universally acceptable.
Both the Jewish and general press have reported on this unfortunate development in recent years. Most recently the Jewish Press reported (2/6/2013) on a conversion, performed by mainstream Orthodox rabbis 20 years ago, that has come under question by Israel's Chief Rabbinate. The article (http://www.thejewishweek.com/news/israel-news/convert-snub-israel-fuels-fresh-anger?goback=%2Egde_1866270_member_211762567) offers details. More outrageously, a 2008 NY Times article detailed the ordeal of a young woman, raised in Israel to an American-born Jewish mother, who was challenged to prove her status as a Jew. http://www.nytimes.com/2008/03/02/magazine/02jewishness-t.html?pagewanted=all
I share this to underscore the point, regardless of how one entered the Jewish world there are those who will ignore our traditions and raise questions. But we do not need to be held hostage by them.
I understand that the reality is that your children may one day find themselves in a situation where they need to speak openly and lovingly to a potential mate and share their whole family story. They will want to enter into an intimate relationship without secrets that potentially may be divisive. For that reason they need to know the journey by which you entered under the tent of the Jewish people. But they, and you, are a long way from that moment. For now they need to know that you are fully, unquestionably, Jewish with all your heart and soul, and that you have raised them to take their own place in the long lineage that extends from Abraham and Sarah to you and them.