The NHS guidance for D&V is not to go to school or work and avoid contact with other people for two days until after symptoms have stopped
https://www.nhs.uk/conditions/diarrhoea-and-vomiting/
Spreading illnesses to a potentially vulnerable baby is not acceptable!
Refer SD Mum to the NHS guidance and explain that basic bio security is important! D&V bugs can be fatal for young children!
At some point OP your child will get chickenpox, or another illnesses and I would put money on SDs Mum insisting that her daughter isn’t exposed to the bug!
Given her daughter has D&V demanding £20 for food seems incredibly heartless… her daughter is probably going to be struggling to eat very much for the next week!
A good parent would want to keep their child at home, let them rest and recover and would want to follow NHS guidance. Not send their ill daughter to a house to spread the infection and have disturbed rest because newborn babies tend not to sleep for 8 hours at night!
Finally imagine how guilty SD would feel if she passed on D&V to a newborn baby sibling that became seriously ill or hospitalised! Babies do die from contracting D&V bugs.
OP you are not being unreasonable!
Offer SD a full week with her Dad during half term or when she is feeling better by way of making up the time! I am sure she would appreciate getting to know her sibling when she feels well!