I am never a fan of renting to the family of a handyman because if something goes wrong you will lose a tenant or a handyman or in some cases both. 

Raising Rents on Long Term Tenants requires 60 day notice with section 8 (while not losing a good long term tenant).

I am losing my mind trying to make sense out of how the bank can take our money for the house which relieve's them from the burden of holding it.

I feel like this is an amazing deal/opportunity to start my investing career and to purchase my first home and don't want to lose out on it.

What the best way to get these rents to market value without losing our long-term tenants or giving them a heart attack?

You can't only evaluate the ROI across the board because if you don't choose a good property, understand the metrics, and have good cleaners and management support, you will lose quickly in Airbnb.

However buying this house will mean that I will lose all the benefits of acquiring a home with 5 or 10% as a first time home buyer.

Losing a job, pay cut, getting unwell, divorce, job transfer and the rest. 

If you find someone to pay more and break your contract you will just get sued and lose out anyways.

Family and business usually don't mix well and when it comes to family losing money, then it really doesn't do well.