Can I get my husband back in the country?

Technically, you should be able to petition the government for a permission for your husband's return to the U.S. However, I cannot give you a definite answer because you did not provide enough information. What was your husband's status in the U.S.? How did he come to the U.S. and how long did he live here? What was the reason for his removal from the U.S.? Was he deported or did he leave on a voluntary departure? Are you legally married? What is the nature of your daughter's handicap? Do you have any medical and/or psychological problems? All this is important and has to be discussed before a correct decision could be made. You need to consult with an immigration attorney.

That depends on why he was deported. If he committed certain crime he would not be able to come back.

It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options.

That will depend upon the reasons for the deportation in 2011.

Yes, if he left on voluntary departure and has no crimes or other issues, it's certainly possible to get a waiver and other prerequisites to come back.

If you are a US citizen, you can file an I-130 petition for your husband, and once approved he will be instructed how to apply for an immigrant visa. He will also need to have a waiver package ready at the time of the interview if not before to prove extreme hardship to his US citizen daughter if he must wait 10 years to return to the US. You should retain an immigration attorney to help with the process.