This answer assumes that your lease falls under the rent stabilization code, since rent control is quite rare these days. The large majority of rent-regulated apartment are rent stabilized.
Who is correct?
The truth lies somewhere in between. There is no automatic right to evict a tenant who has spent fewer than 183 days in a rent stabilized apartment, but a rent stabilized tenant who spends significant time away from the leased premises does run a risk that the landlord will try to make a case that the apartment is not the tenant's primary residence. (Even if the tenant prevails, defending against the landlord's action can be a significant burden.)
For some reason she thinks that you have to go home and sleep there for at least half the year, otherwise the landlord can kick you out.
She thinks this because rent regulation in New York applies only if the tenant uses the premises as his or her primary residence, and one factor specified in the code is whether the tenant has spent 183 days in the most recent calendar year occupying the premises.
Absences for certain reasons (such as hospitalization) may not be taken into account. None of the enumerated reasons applies to an extended vacation except for the last one, and that only indirectly:
such other reasonable grounds that shall be determined by the DHCR upon application by the such person.
So if you went away for vacation, you might be vulnerable to a judge deciding that your absence was not "reasonable"; on the other hand, the judge might decide that it was meaningful.
You might be able to strengthen your case if you go away for slightly less than a year, starting in early July. Then your absence would be less than half of each calendar year. But you might want to talk to a lawyer before considering this strategy, because it may be that your case is strong enough without doing this.
In any event, the code specifies that "no single factor shall be solely determinative," so if you keep all your stuff in the apartment, keep your driver's license and voter registration at that address, and continue to use that address to receive mail and so on, you will have a stronger case. Again, talk to a lawyer before relying on this strategy.
In a comment, you ask
Do you think it's legal for them to be checking the cameras and use that as evidence of me not going into the apartment?
TenantNet, a tenant's rights site, thinks that such actions are mostly legal ("A Primer on Non-Primary Residence Cases"):
Landlords are increasingly using various surveillance tactics to attempt to show that a tenant does not primarily reside in their apartment, and/or that somebody else does. These tactics can include private investigators, hidden video cameras in the public hallways, hiring other tenants to spy on their neighbors and requiring doormen to keep track of a tenant’s coming and going. Most of these practices are not illegal.
You may also want to have a look at the New York City Rent Guidelines Board page on primary residence.
You may also want to look into the rules concerning subleasing rent-stabilized apartments.