This sounds like a habitability issue. If it rises to the level of a constructive eviction you can move, stop paying rent, and sue for costs. However before you take any action consult with a local tenant attorney who can review your case and give you a detailed plan of action. Good luck.
-Michael R. Juarez Law Office of Juarez and Schaeffer PO Box 16216 San Diego, CA 92105 (619) 804-4327 www.jslaw.org Mike@jslaw.org This posting is provided for “information purposes” only and should not be relied upon as "legal advice." Nothing transmitted from this posting constitutes the establishment of an attorney-client relationship. Applicability of the legal principles discussed here may differ substantially in individual situations or in different jurisdictions.
The Landlord's responsibilities are defined in RCW 59.18.060. They need to keep your apartment in a reasonably good condition, including weathertight. Why is there mold in the middle of carpet? Consider the underlying causes and make sure they fix it. Do not think you can use a bissel and get rid of mold, the carpet needs replacing.
It is unreasonable for them to refuse to replace in one room without the whole apartment. It is easier, and cheaper, though not comparatively.
If they do not fix it, then you have the right to remedy the situation through RCW 59.18.070. Then if they do not follow up properly and fix the toxic mold you can break your lease pursuant to RCW 59.18.090.
You might als follow 59.18.100, do the repairs yourself, and deduct it from your rent. But do follow the procedures outlines to the letter.