How can I ask employer about a set schedule?

You don't really have a choice but to be a little bossy/ assertive if you want the problem solved. It's harder to backtrack if you don't set forth the expectations in advance, but you may be able to work with it anyway. Just be aware that you shouldn't overplay your cards. i.e. If you aren't prepared to find another job, don't say you refuse to be flexible. 

In this case, you could try a couple of things. 

1) Remind her you need to be on a specific schedule and then don't let her change it.

2) Be proactive and contact her ahead of time to verify times.

3) Ask her to write up a contract or volunteer to write one- not that the contract will ever really be used as an argument, but because it should help remind her that she has agreed to a specific time.

4) Tell her you have an ongoing appointment every day after work and you cannot miss it. Tell her it's whatever time you're not willing to work after. This way, she'll either have to have you come earlier and help with other things or she'll miss out on covered time... This is a double-edged sword. She may not be willing to move on time and may insist on flexibility on your part, in which case, you'd better be prepared to find a new job.

The other things to think about are what her true motivations here are. You previously said you thought she just enjoyed getting the little one up because she's a first-time mom. If this is the case, then she may just be trying to maximize her downtime or lower her own costs. Is she keeping you late for your benefit because she thinks you need the money or because she wants to have the maximum hours free? If it's free time, perhaps setting a departure time is best. You may get your hours cut some, but you'd know when you leave every day and she'll get roughly the same number of hours covered each day between your coverage and the baby's sleep schedule. Also, her failure to communicate could just be new mom sleep deprivation, in which case, it's beneficial for you to lead discussions and give reminders. 

Keep in mind, you're the "expert" here. She doesn't know anything about hiring a nanny or being an employer. You do. So, it doesn't hurt to say things like, "Most of my previous clients..." or "It's standard in the industry to..." and express what the benefit to the standard procedure is. i.e. "Most of my previous clients kept me on a set schedule, which made it very easy for me to plan my day/ plan my time with the child/ make arrangements to be available." You can soften these statements if you must, but you do have to be somewhat firm. You're setting the tone for the duration of your working relationship.