For context, when is your mortgage on your current home up for renewal?

I assume she's paying her rent, otherwise you'd be evicting her for non-payment of rent, rather than just notifying her that you're not renewing her lease. 

@Jeremy Taggart That was weighing heavily on my decision to sell or renew my tenant’s lease last year and, in hindsight, selling was probably wiser. 1031 exchanges get stressful if/when you can’t find the right deal and I have only worked on other investor’s 1031s as a broker.

It should be really straight forward to not renew their month to month agreement. 

If you do not believe the tenant and you think he swindled you then a notice of non-renewal is appropriate.

The Lease will be due by the end of March.I know that I won’t  renewal them and I also know they don’t want to move, but they can’t afford the rent as far as I could see.So my question is: what if they refuse to move after the 60 days notice that the lease won’t be renewed? 

Parent co-signer a must; Leases are for one year (in SC we do Aug-jul); Rent to a group and the lease says that if someone leaves (graduates) they are responsible for finding the new rental or I will not renew the lease. 

Worst case is the terms are so bad and the common charges go up so high they make the condo units worthless, or the landowner refuses to renew so he can build or sell something more profitable.

In the meantime, they are in breach of contract and risk you not renewing month-to-month. 

You are better off giving a discount for a one year lease, because you have flexibility to either increase rent or not renew at the end of the first year.