Please help me to know if it is allowed for a Muslim to take his wife to USA (precisely) and or any other non-Muslim country for the delivery of the child with the intention of getting the child passport of that country and later on come to that country for the better future opportunities? And on the other side saying that we are doing this because we want to do Dawah work in that country?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Know that belief is the most precious thing in life. It is the real source of eternal happiness. The whole earth full of gold should not be made equal to belief since a wise person considers the ends and consequences of the matter, not only what is at hand. Allah Says (what means): {Indeed, those who disbelieve - if they should have all that is in the earth and the like of it with it by which to ransom themselves from the punishment of the Day of Resurrection, it will not be accepted from them, and for them is a painful punishment .} [Quran 5:36]

Know that traveling to any non-Muslim country will never be a source of happiness but it will only be a false happiness that very quickly vanishes. Thus, the person will come to know that his journey to such countries was the source of misery.
It is known that the Prophet forbade living in non-Muslim countries as he said: “I am exempt from every Muslim who lives among polytheists; their fire should not be seen together.” [Abu Daawood and At-Tirmithi with a good chain of narrators from Jareer ibn Abdullah]

Traveling to non-Muslim countries is dangerous for the religion of the Muslim. In most cases, everyone who travels there is affected badly by their cultural influences.

However, the callers (to Islam) who have good knowledge and strong faith can travel to such countries only to spread Islam. Because the one who has good knowledge and strong faith can avoid the widespread misconceptions and temptations in those countries.

For more benefit on Muslims living in non-Muslim countries, please refer to Fataawa 81142, 81464, 81642, 86405, 377986, 369667, 89879, and 88291.

Allah knows best.