Nanny here. I like 21:21s advice as far as what to say, it's worded well and gets the point across.
While I agree with the idea that you should talk to them and give them a chance to consider everything, I just want you to be prepared, because, there is a very good chance they will not be able or willing to change your total compensation package at this point.
I've made this mistake twice (I know, definitely my fault, especially when it happened a second time). The first time I was a relative newbie and just naive. When I finally made some nanny friends and realized I was being taken advantage of by not getting guaranteed hours or PTO (and, at $12/hr and no raise even after two years of employment, was not being paid well either), I approached MB and asked her if we could discuss things. Her initial reaction was anger that I was trying to "take advantage" of them. Then she laughed about it and told me I could be replaced by someone for even less money "like that." Finally, she told me she wanted me to stay, but they weren't financially able to offer guaranteed hours or PTO.
The second time, I felt a little desperate for the job, so I opted not to bring up guaranteed hours in the interview. That MB told me, upon offering me the job, she'd draw up a basic work agreement with no benefits for the first three months of employment, then, after that, there would be a review, raise, and they would offer me benefits. They were a very affluent family so I figured money wouldn't be an issue, and they offered me a high hourly rate to start, so I took the job.
At the three month review they did give me a $1 raise, bringing me up to $18/hr for one child and no chores required. She also offered 1 week of PTO per year. She did not offer guaranteed hours. When I asked for them to be included, she kept saying it didn't make sense to her, because nannies are hourly employees, not salaried, so why should I be paid for hours I didn't actually work. I feel like I could have gone into greater detail, so she might've actually understood the connection (if you decide not to pay me for two weeks out of the month, it makes it very difficult for me to pay rent); she was from a wealthy family so I don't think she understood what it's like living essentially paycheck to paycheck. Anyway, the hourly rate was high for the area and they ended up not taking too many vacations (maybe 3 weeks total each year) so I stayed with them another year, but it was obviously very frustrating that they were so unwilling to even consider offering something as simple as guaranteed hours.
I wanted you to hear about my personal experience with negotiating for guaranteed hours after you've started working together with a family. In my personal experience with those two particular families, neither of them was willing to consider offering guaranteed hours after I'd already started.
In fact, one more thing to think about: The last time I went job hunting, a little less than a year ago now, I went on many interviews with families. And, I had almost the same experience with every single family: I brought up guaranteed hours and PTO in the interview. Every family acted surprised. Every interview went well overall, and each and every family told me I was the most qualified nanny they'd interviewed, and invited me back for a short paid trial day. And each and every family told me it was between me and one other candidate, but they ended up hiring the other candidate, even though in most cases the other candidate was less experienced, because the other candidate did not ask for guaranteed hours or paid time off. Ultimately I found a great family to work with who pays me a great rate and gives me guaranteed hours and PTO, but it was difficult hearing the same thing over and over from all the other families (we hired the less experienced candidate pretty much for the sole reason that she didn't ask for any PTO or guaranteed hours).
The point of that, is this: for all you know, this family may have chosen to hire you instead of other, perhaps more qualified, applicants, simply because you didn't ask for guaranteed hours or PTO, and they thought they'd be saving money by hiring you. Obviously I don't know that that is the case, but I think it's definitely a possibility.
So again, it IS worth talking to them, and maybe they will be different than most of the families I've experienced, and maybe they will say "you're right, this is your livelihood and we care about you, so let's draw up a contract with guaranteed hours and PTO right now!" But, they might balk, and they might stall and say they need to think it over, or they might just flat out say no. So, just be prepared for the possibility that you might need to walk away.
I know finding a family that is just the right fit in terms of how they raise their children and their location and schedule and all those other factors is difficult enough, let alone finding a family who understands they have an obligation to their nanny to give her a solid paycheck so she can pay rent and bills every week (or every two weeks or whatever is agreed upon). And I know it seems daunting to find just the right family; after two months of interviews and trial days, and every family saying "you're great but we found someone cheaper," I was extremely discouraged. But, eventually I did find the right fit, and so will you. Good luck.