Lydia's your housecarl (bodyguard), and lives in Breezehome. Outside of possible console solutions, there's really only two ways to get her to move elsewhere:
- Recruit her into the Blades; my understanding is that she'll then make Blades HQ her home when she's not following you.
- Marry her and move into another house you own. Not really an option for you at this point, however, as you're already married.
Your only other option, I think, is to simply accept that you and your wife have a live-in bodyguard thanks to your position as Thane of Whiterun. It's not really anything for the wifey to get upset about -- Lydia even has her own separate bedroom! In fact, having a housecarl is definitely a sign of honor and privilege, so your wife should be rather pleased with the situation!