Can I renew my green card if my husband is in jail?

Yes, you can. You can "self-petition" for your green card. 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. (S)he would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

Generally, in this situation, a person can file a joint petition with his signature, or, the person can file for divorce and then file the application without his involvement.

You have quite complicated circumstances. It's not clear: do you have a conditional permanent residency's card? If yes, you probably may apply for removing your conditional status, provided you show the proof of marriage which does seem survive your in-fighting. You need to prepare many required documents and send them with the petition. But, this petition should come from your husband, who is currently in jail. That certainly complicates the matters. You could, probably, proceed under a different avenue, through VAWA or U-visa. Those are very complicated and you should enlist at least a help of some non-profit agencies helping women causes. They might, and should, help you for free. However, if you want to preserve your marriage for the sake of your son, working with your husband in prison might be a way to go.

Is your status conditional? If so, you do not renew your green card. You remove the condition. I am assuming your husband is a USC. If so, he can stay in jail for as long as he wants to and not worry getting deported. That is one of the privileges of being a US citizen.