Hi and welcome
Your living situation is very unusual, so I do understand why social workers are going to have questions. The SW has no idea of your cousins feelings, or intentions and no idea that she wouldn't just decide to move out without a very good reason. So they do really need to probe and get as much information as possible.
If you are turned down by this agency, there is nothing to stop you approaching other ones, and I would do that if you are committed to trying to adopt. I have no idea how other agencies might react but I think your best chance of being accepted is by acknowledging that your situation will be concerning, saying that you understand why this is but have thought long and hard about how it would work, and countering their concerns.
Having an actual plan in place for if xyz happens, is likely to be more reassuring to a social worker. Do you have a plan in place for what would happen if for some reason, seen or unforeseen, you will be living alone there? That really isn't impossible, even if it's unlikely, because things happen. Plans for finances etc? If you can show that you have the incomings to match your outgoings and provide for a child now, AND you have a basic outline of a future financial plan for if you are living in the house alone/being able to afford to live in another 2 bed property alone, then I would hope that would be reassuring enough. My assesments were based of the income that I currently had and would continue to have, not off income that I would have if I adopted.
I think they are also likely to have questions about how the relationship betwen your cousin and adopted child might work. Are you still doing most of the caring? Importantly, what happens if your child has difficulties which your cousin finds really difficult to live with, or can't live with anymore? What's the plan if either of you meet someone special and want to live together? Etc etc.
Health wise, if the prognosis for your future is good with a mostly normal life expectancy, then that should be okay. If your future is uncertain they will be worried. They are likely to have concerns though because heart failure is serious. A report from a cardiologist might well be needed. As well as a thorough assessment of how your condition affects your life and how you deal with it, and how a child will impact on it and how you would cope with the demands of child raising. People with disabilities do get approved to adopt, all the time, but expect and prepare for a more in depth assessment.
My assessment (I was 28 and single when I applied to adopt my first) had a lot of what ifs. And the assessment does need to have those questions, for the childs sake. They really needed to know how I was thinking and how I was planning, what my expectations of the future were and whether they were realistic, how flexible I was and so on. So I was asked how I would cope if I had to give up work because of my childs needs (which ended up really happening), what would happen if i met someone 'special' and so on...what happens if my child doesn't like/want me being gay was my personal favourite 'what if' question(!).
Realistically, SS don't tend to like non-conventional situations. It's always harder trying to adopt in unusual situations. I always do suggest trying more than one agency anyway. I can't say whether or not another agency will be comfortable with your situation, but going in armed with good responses to concerns is IMHO the best chance with a second agency. You may find some VA's are more accepting than most LA's
Best of luck to you