I got through 6 months of chemo (Jan-Jun) without infection. The oncologist prescribed Neulasta because my neutrofil count dropped very low with the AC treatment. Apparently Taxol is not so hard on the white blood cells so it wasn't needed for the second three months of chemo.
I did lots of handwashing and avoided sick kids, public transport and shopping malls during the most sensitive weeks.
I had a dental checkup before I started chemo. I couldn't have a flu shot before because it was January and the new season vaccine wasn't available.
I think you're right to be concerned and it would be worth taking drastic action (face mask if one of the kids comes home with a cold, lots of handwashing) to avoid a hospital stay. Download one of those posters that show how to do effective handwashing and teach your kids how to follow the procedure.
Wishing you well - I hope you manage to avoid all the serious pitfalls, as I did. And I hope your support network comes through big time!
Gillian