Hi Katherine,
You are in a difficult spot. The State of Vermont is one of, if not, THE WORST state to evict a tenant. If they contact legal aid this process will take at least 4 months, maybe up to 8-12 and will potentially cost you 5-10k. My advice:
1) offer the tenant a cash payment to vacate within a week or two. The amount should be negotiated by you and them. Could be $500-$1500. Don't give them a dime until they have completely vacated and signed a contract giving up their rights to the apartment. This may seem like a tough pill to swallow, and it is, but it will be less stressful and much cheaper than the eviction process, trust me.
2) if they refuse to leave after being offered the money contact an EXPERIENCED eviction attorney who charges a FLAT FEE for the eviction. Otherwise you may end up hiring someone who will cost you a fortune and/or make mistakes which will drag things out longer. This is a very important point. Vermont courts are not forgiving to landlords and the service process must be adhered to entirely by the book. I would recommend contacting Angela Zaikowski at the Vermomt Landlord Association, she is one of the best and literally wrote the book on Vt landlord/tenant rules. She charges a flat fee I believe to handle evictions.
3) in the future screen all holdover tenants as if they were new prior to purchasing the property or have the current owner kick them out. People usually are selling partially because they have issues with tenants they don't want to deal with.
4) don't waste a single day. Start the process now and if you made mistakes start over and don't relent until the problem tenants are gone.
Good luck