Honestly, OP, I would just tell them exactly what you've said on here. That work is essentially your one bit of normality in an otherwise stressful situation where you are allowed to focus on something other than your DH and his illness, and it's beneficial to your mental health to retain that structure and outside interest.
You could perhaps ask them if they have concerns about your performance or whether there are other reasons for wanting you to take time off, but as you've said that they're generally supportive, I suspect that they just haven't quite grasped that continuing to work is what you actually want. They might think you're soldiering on because you think you have to be strong, don't want to let them down etc, and so they're trying to make it easy for you to take the time by forcing the issue. Once they realise that staying in work is genuinely what's best for you right now, they might back off and leave you to it.
I think the only way is to have an honest conversation about why they keep pushing the issue and whether it's due to concerns about you being in work (in which case, can those concerns be addressed somehow) or whether it is about what they consider to be in your best interests (in which case, you need to get them to understand that taking time off won't help you right now).
I would probably put pressure on a conscientious employee to take time off in your situation as I would want them to be in no doubt that it was OK to do so, but if they explained to me - as you have explained above - that maintaining the routine of work was genuinely helpful to them, then I would of course respect their preference.