I also have an interest in furniture and hardwood restoration.

This was the clause in the lease regarding termination:In case of any termination of this Lease or termination of the Resident’s right to occupy under this lease, byreason of default of Resident or non-payment by Resident, Resident will indemnify Landlord from and againstany loss and damage sustained by reason of any termination caused by the default of, or the breach by, Resident.Landlord’s damages shall include, but shall not be limited to, any loss of rents, accrued but unpaid prior totermination; all costs and expenses reasonably incurred by the Landlord to restore the Premises to the samecondition as they were at the beginning of the Lease, including cleaning and painting (reasonable wear and tearexcepted); any costs reasonably incurred to advertise and relocate a new Resident, including broker's fees;moving, storage charges, or any other expenses, fees, or costs allowed by law, incurred by Landlord in movingResident’s belongings pursuant to any legal proceedings and as allowed by the court.

The contractor you choose should be able to do the restoration within the budget the insurance company comes up with. 

Mine says they'd have to restore it back the way it was. 

My family has a restoration company so they helped do a lot of the work.

They might charge you 50% more for "restoration cleaning" but much cheaper than new carpet. 

I refused because I am treating his wife's lease as a completely new one and processing it as a standard tenant move out/move in (ie. restoring property to previous move in condition) Am i doing the right thing?

We'd like to do the renovations ourselves so we can: learn how the guts of a house work to become better investorscapture more of the equity with our sweatpay for the project as we gosave money on material costs w/ CraigsList and Restore purchasesbecome more flexible, capable humansWe also think it would be fun.After 2 years, we will try to sell each unit individually as a condo.

How do I figure out what my property will be worth after updates when using the BRRRR method? I'm looking at my first property, a triplex for about $55K. I haven't toured it yet and not sure how much updating it would...

They might pay PART of their rent,  but the government pays the rest or owns the property.