Salam to Respected Alim, Is is Allowed to have Nikkah with the same person again?

We had done a secret Nikkah (properly in presence of an Imam and witnesses) because our families were not agreed and it was only Nikkah as I and my wife did not spend any time alone in a bed room or had an adutlry, so there is no baby or such thing. Our families are agreed now. But we can not tell them that we have done it already because they will not owe us again due to this in-obedience and will never see us again. Can we have one more Nikkah official in presence of families? Is is Allowed to have Nikkah with the same person again, coz we can never tell them we had done it before? Please help me in this confusion. May Allah give you its AJAR.