NYC Tenant Rights - Compensation / Eviction pls help

My parents ( 1 retired senior citizen , 1 breast cancer survior and a minor son 16 year old) resides at a building that was built in 1910. It is consider regulated as Rent Stabilization I believe. We are located in NYC, the neighborhood has become a trendy hot spot and off course it would be the landlords dream to evict or have the old tenants moving out without compensating. Well my parents ran their mouth due to frustration that the apartment is broken up and needed renovation they asked the landlord to offer compensation, they agreed verbally on 15,000. Now this is the thing, I doubt $15,000 will last at all due to nyc living expense is so expensive, our rent is 800 a month for 2 bedrooms so its not bad. I do not live with my parents they live with my younger brother. I called the landlord and got the offer jacked up to 20k because I said they misinterpreted about getting compensated and now the landlord is saying she was planning to let us know she wants to take back the apartment for herself and she as the landlord has the right so. She does not even have to compensate us and its because of good will and since we are long loyal tenants she is compensating.

Does she have the rights to evict us ?

please let me have your opinion.

Per the housing laws:
Reasons to terminate:
Occupancy by owner or member of owner's immediate family.

(1) An owner who seeks to recover possession of a housing accommodation for such owner's personal use and occupancy as his or her primary residence in the City of New York and/or for the use and occupancy of a member of his or her immediate family as his or her primary residence in the City of New York, except that tenants in a noneviction conversion plan pursuant to section 352-eeee of the General Business Law may not be evicted on this ground on or after the date the conversion plan is declared effective.

(2) The provisions of this subdivision shall not apply where a tenant or the spouse of a tenant lawfully occupying the housing accommodation is a senior citizen or disabled person, as previously defined herein, unless the owner offers to provide and, if requested, provides an equivalent or superior housing accommodation at the same or lower regulated rent in a closely proximate area.

So yes, she can ask then to move, but only if she finds equivalent housing for them at the same rent. Her offer of money could be included in this equivalent housing. If she is offering $20k, that would compensate for the higher rents for how long? (For instance, it would pay the difference of $400 rent a month for about 4 years). How much under market rent is their rate?