1) I would wait till Dec to divide your plant its 90F outside today. 2) it is probably a seporate plant (with yellow flowers) will be able to tell this fall if divide that plant. 3) the plants will cross polinate But not sure of genetics of flower color of this species. I would expect a varitie of flower collor's on NEW plants grown from the seed. the ORIGINAL plants will always be of the same color

You can remove a division now if you want. Many plants might not make it right now, but hollyhocks are tough. The parent plant really shouldn't be affected at all by removing a small rooted division, and the division should be fine if well watered. Placing the new plant in light shade until established wouldn't hurt anything either.

You mentioned the root not having time to heal if the division was done in the winter. Roots continue to grow in winter. In many cases, root growth actually increases during late fall and winter. For most plants, divisions and transplants are best done during mid to late fall (your colder hardiness zone may change this some) or early spring. Some plants, like hollyhocks, can take it just about anytime with a little extra care.

I have bought a pair of two holly hawk roots from a home depot store. I have a place with rich soil in which to plant them. I was wondering since they were bought at a box store if I planted them this summer if they will actually bloom the first year being planted. I know plants started from seed may not bloom the first year.