It's not silly or unreasonable. It's a dilemma.
Call your Ped for their take. They know your daughters weight situation better than anyone here.
I had to cx a LOT of stuff this year, because another respiratory infection could have killed my son. Stuff other people would find no big deal, but with compromised lungs, 2 months total (week here, week there, 5 weeks In one shot), his lungs and immune system were too fragile to risk.
If your baby is underweight your Ped may well have you avoid intentional repeated exposure to someone with a nasty stomach bug. Exposure, btw, is not a 1 shot thing. Contagion also varies. They may not have been exposed at all previously, or had a mild exposure. Going into a house where there had been intense saturation of the illness responsible may be risk free (only contagious at the beginning), or may be risk heavy with the viral load at its most potent. With these types of things (unidentified), no one knows. Everyone may get it anyway, or not at all.
My .02 If your baby is underweight and looking at hospitalization for this kind of illness, running the risk that they MIGHT not be contagious, or MIGHT already have it seems... Dumb. There are so many things you CAN'T avoid (like possible exposure before you knew, daycare, grocery stores, whatever), that intentionally placing her at risk? That, to me, is like saying "There's always drunks on the road. So why not drive drunk?"