I am sorry for your husband's medical problems.
Any surgical procdure comes with the risk of infection. However, if the hospital/doctors failed to properly treat the infection, you might have a case. Only a medical malpractice attorney in your state can make that determination.
When you say '3 days later he started getting ill,' was he still in the hospital at that time or if at home, did he return to the doctor immediately, or the ER?
You state on May 3 he was readmitted at which time they determined he had a staph infection and began treatment which continues to the present and that he required additional surgery.
You should take all of his medical records to a medical malpractice attorney in your state who will arrange to have his records reviewed by a medical expert to determine if malpractice ocurred.