My daughter lives in Cairo and there are no official Shia nikah authority that perform official Shia nikahs. Therefore we shall do the official nikkah the Sunni way, and we will recite the Shia nikkah ourselves at home. Is this ok according to Islamic Laws?
Secondly my daughter will travel to India for the wedding after a few months and we want to do the official Shia nikkah in India. Is there an issue/problem in reciting a nikkah more than once?
The reason we are performing the nikkah in Cairo so that we can get the nikkanama document in order to start the visa process for my daughter to travel to the groom's country.  

There is no difference in the nikah contract between sunna and shia. However, all what you said is OK.

My daughter lives in Cairo and there are no official Shia nikah authority that perform official Shia nikahs. Therefore we shall do the official nikkah the Sunni way, and we will recite the Shia nikkah ourselves at home. Is this ok according to Islamic Laws?
Secondly my daughter will travel to India for the wedding after a few months and we want to do the official Shia nikkah in India. Is there an issue/problem in reciting a nikkah more than once?

Both are fine