i'm a (mostly) single mom, and i am a postpartum doula. i became a postpartum doula first because i knew that the on-call demands of birth work wouldn't be do-able without reliable middle of the night childcare. postpartum work allows me to make my own schedule - and so, for you, if there are two days a week you *know* you can have childcare, than you only work those two days (maybe 8 hour shifts, you know?).
i originally had planned to bring my daughter with me who is 4, but after a little work (i've only had two clients, and the second was more of a long-term nanny position in which i did bring my daughter), i realized that while my families were perfectly fine with it, *i* was not. now, 11 months old is much, much different than 4, and my 4 year old is pretty needy, socially, and thus there are a lot of reiterating rules and such that i'd just rather not do in other people's homes. an 11 month old can be contained/played with differently, and you might be alright....so, the way that i would present it, would be "i can be there on x day and y day, and if you need help on z day i can be available but i will have my daughter with me, and i want to make sure that you are getting one-on-one care, so it usually isn't my policy to bring him/her along. however, if you really, really need help, i can be available. i would not bring my own child within the first week or so, though.
another thing you could do is look into what kind of postpartum work you really want to do - there are some ways in which you can be useful without necessarily needing to do, say, overnights and intense home visits. what if you facilitated new-mom groups that met somewhere, and you could charge a fee...what if you taught a class and partnered with a childbirth educator, etc. you could even look into breastfeeding support, and i find that when you offer a specific service rather than a general practice, it's a little easier to drop some of the required flexibility for traditional postpartum care.
and also, the baking/culinary aspect? USE that, mama! people will hire you in a heartbeat! you could even teach a class or like, offer a meals service (and that would make a great new-mom gift from her family if the family isn't going to show up with meals every day).
you make your practice, you know? take a look at what you've got and what you want to be doing, and make a rough plan. talk to people. meet with other people in the field. you can absolutely do this.