I think the act of opening an LLC on H1B is not the issue, but if you show any income/profit on it, that's when you will run into legal issues, this will also be vitally important if and when you are applying for your Green Card as you could be in muddy waters regarding your eligibility status during the time you were operating the LLC.

Also if you have even a single founder who is a US citizen or Green Card holder, you could get a relative of yours who is not in the US to be an additional founder for the LLC. This way you (your family) retains control of the company. They will need to apply for an ITIN number in this case. I can vouch for the legality of this option as we had hired a lawyer and I got my dad (non US citizen) to be a part legal owner of the US based LLC that was formed.