Legal heirs derive title to property, to the extent, the deceased propositus had. If the title was partial,tainted, defecttive or encumbered, then the derivation too will have these attachments.
In your case, since title is claimed through the deceased father and not independently, the said title is encumbered to the extent of the lease period as well as rental agreed upon. Unless there is a specific provision for enhancement of rent periodically, no enhancement can be claimed from the tenant, irrespective of market conditions. You may see the plight of landlords throughout the country who have let out premises and quarters to nationalised banks, insurance companies,post-office, telephones etc. Nationalised banks are the worst offenders in this respect by their cunningness while entering inti lease. The premises are never got back by the landlords and the rent paid is not 'peanuts' as you choose to call but rotten peanuts.
First of all take steps to get the property mutated with the revenue/municipal authorities, in the name of legal heirs and then ensure payment of rent to the legal heirs, individually or collectively, as decided amongst the legal heirs. Well before the expiry of lease, issue notice of vacation, carefully observing minimum notice period prescribed, if any. Don't offer renewal. Make the tenant seek renewal and negotiate orally. Of a deal is struck, then get written proposal for extension of lease on terms agreed mutually.
If no deal is struk, stick to your demand of vacation. Then only better offer will emerge. If there is an arbitration clause, promptly submit the dispute for arbitration.If there is no such clause, you may have to file a suit in jurisdictional court, which entails payment of court fee, and seek guidance of your lawyer.