What happens if one of my breast implants hardens and the other doesn’t? Do both need to be removed?

Implant won't harden. Implants don't get hard, ever. But the scar around them can tighten, thicken, and make the breast feel quite firm (capsular contracture--cc). When cc occurs, it can be due to an old silicone implant rupture (the newest ones don't leak and rupture rarely), bleeding around one side, bacteria (not infection) around one side, such as from dental work, etc. If old replace both. If new, correct the cc!
How old are implants. This answer is complex and requires analysis of several issues such as: how old are your implants? Size satisfaction? Degree of sagging? For example if your implants are only one year old, i would advise single sided replacement but if 10 years old, i would probably consider remove and replacing both with replacement or fat grafting.
Sort of. One breast with capsular contracture would best be treated with surgery to remove the implant and scar tissue surrounding it. While you're in the operating room and under anesthesia, it makes sense to exchange the other implant for a new one, too.
Capsular Contracture. This is called a capsular contracture and there are few solutions to this problem other than removal of the capsule and replacement of the implant.