Can i quit from my employment contract for 1 year?.i am in J2 visa and i have valid EAD to work in USA?

i am an employee of a indian consulting company and When i started my career with them ,i worked for 2 and half months ,within that my 2 year old baby was hospitalized due to asthma problem and so i was to be with her in hospital for few weeks .so i told my client whom i worked for & they could understand & accepted my job leaving letter .but my employer scolded me ,atleast you must give 15 days notice to us to quit from the job. how can i give notice before 15 days ,when my baby is hospitalized?. how could i know whether she fall ill and be serious. After leaving from my job ,i 'm in home with my baby for 5months and still being at home. now i got a good offer from another consulting company who treats employee well. i dont want to continue with my previous employer.can i move to newer employer?.whether the previous employer will sue me with the contract signed paper?. i didn't go any training classes with them. they not even paid my per diem as they said . please help me .

Take leave of absence....that way you officially have 2 jobs, and then you can terminate on job and keep the other job later....