Maybe she just resents the toddler getting all the attention? Easily done, as they're so cute at that age. I don't see why she's expected to play with the baby.
It could also be that she lacks confidence with small children - so perhaps an adult could involve them both in an activity - or demonstrate ways to respond? Ignoring isn't nice, though, so perhaps she could clap hands or peek-a-boo for a few minutes.
My grandson, at that age (having been an only child) resented being continually pestered by a small half-brother, spending weekends with his dad.
The soap thing - we've all had sore hands this year. I've bought two foaming soap dispensers for the guest bathroom and toilet. They are quarter filled with moisturising hand soap, then topped up with water. The foam, a weaker solution, is kinder. We use O'Keeffe's working hands before bed.