J.C.
I see this is your first baby. You're pretty optimistic to think that you can care for a baby while getting a full day of work done, unless you have the type of job where you can get things done at night after your husband gets home. You get a baby with colic or one that doesn't nap (like my first) and believe me, you will be lucky to get one shower during the day for the first few months, let alone a luxurious day of typing away while your baby slumbers nearby. (hah!) Or you could get lucky and get nice, long naps. No way to tell in advance.
I'm sure it's probably legal and I think it's pretty common to expect you to either be in the office or in an environment where you aren't trying to do two things at one time if you're being paid for your time. I think you should not lie because (not to be unkind, but I think it's important), every woman who does a half-assed job while "working at home" makes it harder for the rest of us to negotiate family-friendly work conditions and be taken seriously. (I work at home 2-3 days a week and I've gone without child care only once or twice when a child was ill, and I've been open with my boss about what's going on on those days.)
What I did after my first son was born was negotiate a 4-day part-time schedule for the first year. Some woman work 4 10-hour days, with some of those hours in the evening. You might also wait until the baby is born, get a feel for his/her schedule, and then hire someone with less experience to be a mother's helper for the peak hours when the baby needs more attention. (if he tends to sleep for 3 hours in the afternoon, you could hire a morning sitter for a couple of hours where you could get some productive work done.)