I was where you are, OP.
First, you have to prioritize your health and your sleep. And start drinking more water even if that means cutting short outdoor activities with the kids.
Second, small changes: do two push ups tonight or one squat. Build on that. I actually used to do my elliptical for one minute just to get back into the habit of exercising.
Third, institute a 30 minute quiet play with the preschooler when the baby is napping. Going eight or nine hours without a break is hard for everyone.
Fourth, make sure your weekends involve something joyful.
Good luck. Being a good nanny is a hard job!