Maha Lakshmi's sons are Kardama, Chiklita and Apa (water). There may be more, but I am not sure. Maha Lakshmi's father by adoption is Sage Brighu (not Kardama). That is why she is called "Brighu nandanaya".
There are no progeny born to Vishnu and Lakshmi
Vishnu and Bhudevi had a son, Naraka (asura). Naraka was born when Vishnu took Narasimha avatar. Because of his rakshasa qualities he was cursed by sage Vashistha and was killed by Krishna (another avatar of Vishnu). Father killed the son - there is no nepotism when it comes to protecting Dharma.
Brahma is not a son of Vishnu. Yes, he appeared in the lotus that grew out of Vishnu's navel. But Vishnu was not aware of it nor did he try to create Brahma. Afterwards Rudra appears and teaches both Vishnu and Brahma that, he came from the same entity that created the Universe, Vishnu and Brahma. That formless supreme is NARAYANA. These three and Shakti are the physical manifestations of that Supreme God, JUST AS THE WAY YOU AND I ARE. Their role is to run the universe with different responsibilities given to each - Brahma (creator of things -tehnologist), Vishnu (jagat Prabhu) Shiva (jagat Guru), and Shakti (the power without which no God or humanbeing can live or sustain). Our role is to be actors in the great drama of Narayana and the manifested Gods.