Welcome to the forum instantcoffee! Well, if you will be working while pursuing your PhD, you´ll quickly find out of the low salary here compared to New York City and also the low purchasing power of the reais. And the high cost of living in São Paulo will further aggravate your financial condition and then you have 2 kids which will also further degrade your ability to cope with the high cost of living. Sorry to start with a sad note but unless you have already enough money saved up to pay for your education and then some, it will be very tough. I don´t have kids and not married but I do help a Brazilian family on their education: 1 adult and 2 children ages 7 and 9 whom I send to private schools. Private school is the best way to go for the children because of the bad quality of public school instruction. That is also expensive including the university tuition I´m paying. School supplies are very expensive and you have to pay for them. Clothing also is expensive with bad quality compared to the US. PhDs pay tuition approx about R$75,000 a year according to a friend of mine. Foreign graduate and post graduate students are allowed to work. Just get a permission from the Coordenação Geral de Imigração (CGIG), at the Ministério do Trabalho.
That´s just a general aspect of it. Other contributors do expect more questions from you so fire away. I´m sure they´ll also be glad to help you!
robal