Family cohesion during a 10 month study course

Hi there,
We are lost and feeling very discouraged right now - here's our situation, I hope someone can help!

I am a mother of 3 children, ages 5 month old, 4 yrs old, 7 yrs old. I am enrolled in a course in Bergamo for this September - it is 10 months long. At the end of it, I will be a trained Montessori teacher. During this time, we planned to hire a nanny there to help care for the children while my husband works from the apartment (he is a programmer who can work from anywhere). We are all Americans.

Initially we thought we would get the familiare al seguito visa at the consulate. However we could not figure out a way to get the nulla osta, and the consulate did not give any advice. They simply said they could not assist us with the family visa. They offered an appointment for me to get a student visa.

After lots of research, I determined we could try the family cohesion. But I'm concerned that my course is only 10 months, and I think we need my permesso di soggiorno (once I get it in the country) to be for at least a year. I see this in some websites but not all. The other challenge is I cannot find any experience where a family successfully did family cohesion. Do we all fly in to Italy together, and I enter with my student visa and they as American tourists (they don't need visas as Americans)?

We have savings set aside from selling our house to cover our costs in Italy, but I don't know if that constitutes as income for the family cohesion.. So many questions and we have barely 2 weeks left.

The biggest challenge is that we have to sign a lease and pay a deposit on the apartment (almost 5000 euros). If we get turned away at the airport or later at the post office/questura, we would lose all that money I think. We can't do the family reunion option because my kids are just too young to be without me for 4-6 months (especially my 5 month old who is still nursing)..

Any advice, ideas, contacts would be most appreciated.