If she's saying she's too tired to work then at least she's not putting your dd in danger but if she's not coping perhaps she shouldn't be working at all.
ssd no offence but I would be worried if someone was looking after my dd and several other kids on 2 hours sleep, but i guess you know what you can handle.
I know someone who crashed her car, not thinking straight due to exhaustion, her ds still wasn't sleeping through at 1 yr.
I know it's hard though, when you have a child the unexpected happens, I had to cancel work once because dd kept me up all night. I knew I wasn't fit to work, as my job takes a lot of concentration. I felt awful about it as it is unprofessional, but I felt that going to work in that state would have been more so, I couldn't risk making a mistake. (I'm a complementary therapist).
Don't people who go out to work just ring in sick when they've had a really rough night?
It's awkward when you work for yourself and people are relying on you (I'm self-employed).
You do need someone you can rely on though, if she keeps letting you down. My dd still wakes up several times a night & I'm working part-time but I keep thinking I might have to give it up if she doesn't start sleeping better soon, as my heads foggy.
Mind you lots of women work full time and have babies that wake in the night. It's amazing how you find the strength to keep going isn't it? I suppose it depends what your jobs like too.
If she can't get dressed in time for work, then she's not fit to be working.
Sorry this is a bit long & waffly.