I know logically that staying in my current home and renting 3 of the rooms is the best bet financially but frankly the older I get the less I'm able to tolerate roommate situations. 

Be tough and righteous and confident.And by the way, fair housing laws don't apply to roommates, normally.

I lived in one side with a roommate and rented the other side.

If you didn't mind the resident faces changing occasionally, you could probably keep it rented year-round furnished.I managed a property in Santa Clara, and learned that Indian techies would lease a place as roommates, then they would rent more floor space to more of their Indian techie co-workers and friends (normally, all single males). 

Also, research the owner name in the landlord tenant court search site; the applicant may have lived with somebody and was not on that lease, and there could be evictions for the roommate with that landlord and due to that set of circumstances your applicant might have been part of an eviction of that other person.And I suspect that you may have fallen for the applicant having some other person pose as the prior landlord - you first have to learn some of the methods we use to establish whether a reference is legitimate or not; this post has already gone on long enough and that is something to be learned for the next time anyway.

However, I would usually want to vet and approve their potential roommates. 

At this time, her prospective roommate's income is pretty low, but they have no debt that I am aware of.

This renter has recently violated the lease with an unauthorized roommate which would cost me more to evict and most recently threatened if I raise the rent at all "he and the next door tenant will move, but he will fight it I am most certain!

Not sure if this is the right forum but I just bought a single family to house hack using fha in Lancaster City, PA area and I'm looking for roommates.

One issue is one of the students previous landlords said he and his two different room mates left the place in a very dirty and poor shape.