When I try to make one villager heal another, they misunderstand and either go off indoors or get offended if they are the same sex.

How do I persuade this randy lot that I want the sick healed, not ravished please?

I have lots of kids and my elders are still sick.

There's a difference between being "sick" and being "weakened" with respect to a villager's health. A doctor can heal a villager only if their status is "sick" (and not weakened). A weakened status can be due to on-the-job injuries, prolonged sickness, or starvation. The only way to improve a weakened villager's health is to make sure that there is plenty of food, that your villagers are researching better medical technology, and switching them to a less hazardous occupation, if possible.

Thanks - I didn't realise that.

Since they keep going indoors, I suppose there is another possible reason for being 'weakened'.

loss of food?