You write well. Your clarity magnifies several issues that you are dealing with. First, is the issure of the poor home health aide and the poor agency that does not
stand behind their work by sending in a replacement when the aide is absent. Many home health aides work day and night and sleep whenever they can. The issue of poor home health aides is a societal problem. Unfortunatelyl it gives the whole profession and the many wonderful people within it a bad reputation.
The second problem you reveal, also an attitude of society, is that your boyfriend expects you to care for him, unpaid, for the other 108 hours a week and still hold down a job. Could anyone do that without feeling burdened?
Another difficulty is that whoever set up your care plan did not have a good vision of care that would be helpful to you or to your boyfreind or to society. Care is more than a "body for a buck." In additon to caring for the frail person's physical needs, we have to consider the caregivers, the relationships and the connections that make life worth living. If we kill the spirit, then we all become the walking dead and no one benefits.
In some states, if your boyfriend is on medicaid, and if there is a waiver, you might be able to be paid. Also, if you can express your issues clearly without blame, you might make a proposal to the agency. Perhaps you could be signed up with them as replacement help.
You would benefit from advice from a professional who practices where you live. You might want to try the Area Agency on Aging to assist you or to reccommend an elder care attorney, geriatric care manager or social worker who could advise you on the rules for your state.
And finally even if you can't work out all the details of proper compensation for your care, try to help others. Write a blog, join a chat room, contact the National Family Caregivers Alliance. Speak out, not with anger, but as a person who needs help and wants to contribute. So much of our health care crises is a problem of care. We need a better vision so the people who can help us proceed will want to help.