My daughter hit my cold sore with her hand. But I washed her hands right away. Is there anyway that she can contract the hsv1 virus?

Cold sore. You did the right thing by washing her hands. In general the virus is contagious but you did every thing you could to prevent it spreading. The longer your cold sore had been present the less likely it is for you to spread it.
Yes and no. Almost everyone contracts that virus, at least we hope so. Once it is inside, it hardly ever causes problems. The first time it happens is worse than any others. Those "any others" are with us forever.

Related Questions

If someone w/ a cold sore on their chin & spit on my skin near my eye while talking & I used hand sanitizer. What are my chances of getting hsv1?

Herpes Virus. Herpes virus is spread only through direct skin-to-skin contact or mucous membrane contact. Herpes simplex virus enters the body through broken area of skin or intact mucous membranes. Thus, it is very unlikely that you contacted hsv 1. Read more...