I've dealt with a lot of college students and co-signed parents (I managed a lot of college rentals in Downtown Charleston, which has The Citadel and College of Charleston). It looks like you have multiple issues going on to work through so I'll try my best to help out. Sorry for the ranting!
For the repairs during an active lease. Are you charging them rent for the summer months? Even with an August 12th occupancy date? Since the lease started May 1st, even if they're not living in there right now, they can move in whenever they want. You may have put yourself in a bad spot by having a property under reno during an active lease. What would you do if one of the Tenants decided to move in tomorrow? There's a gutted bathroom and various reno work throughout the home. Legally you can't stop them from moving in regardless of the condition of the home.
For the mom trying to get out of the lease. Is your lease a Tenancy in Common or a Tenancy in Severance? Basically, did they all sign the same lease, or did they each sign their own individual lease? If they signed individually, then you may be legally required to refund their deposit and remaining pre-paid rent. If they signed on one lease together, then all tenants must agree to release them from the lease. An updated lease would need to be sent out removing their name from it and all remaining tenants must accept the responsibility of the full rental amount. Most likely, they don't want their rent to increase because one wants to back out. So they'll be stuck in the home until everyone agrees to release them from the lease. That takes the responsibility and liability off of you.
Lastly, did the parents sign the lease agreement too? And is their child also signed on the lease agreement? If the parent isn't signed on the lease, then the parent is unable to make that decision. Their child is a legal adult signed into a contract. Per law, the child is the only one who can make that decision. If the parent did sign, then you need written documentation of their request to terminate from both of them.
Don't let the parents push you around. I understand they're doing the best for their child, but their child is an adult and, legally, must be included in these communications and is ultimately the decision-maker as they are the person living there.
Moving forward, I'd recommend not starting a lease until the home is renovated, cleaned, and move-in ready. To prevent these sort of situations. I'd also recommend that guarantors apply and are approved by you, but do not sign any paperwork. If a guarantor asks, just let them know you have their information on file to contact them in case the tenants don't pay, but legally, the tenant is fully responsible. This prevents you from being able to go after a guarantor in collections or filing an eviction against the guarantor, but it allows you to tell the guarantor that you can legally only talk to the tenant. Preventing the parents from butting in like this. They can talk to their kid all they want, and tell their kid what to do. They just can't tell you what to do.
It's a sticky situation to be in, but depending on how the lease is set up you may be able to get through it pretty quickly. And hopefully this helps with planning for your future leases! College rentals can be stressful, but I've found that as long as you are open and upfront with college students, they're pretty understanding and flexible if a problem comes up!