I started with a family, and six months later the parents split. I stayed for eighteen months more and it was tough. The kids were school age, so more prone to their own opinion on things, so it was important to manage it eg.
"Daddy is always late, he doesn't care about us"
I would answer that public transport must be bad or that he was stuck in a meeting. As tempting as it was to join in the general disdain for their father it is so important to remain neutral.
That said, my MB paid my wages. She paid for everything actually, and so my job security was solely dependant on her. DB, instead of telling me to do something, now had to ask. I had the option to say no. So the dynamic shifted a bit. That took a bit of getting used to.
Depending on the type of personality your MB is, she might talk to you about everything or keep it all in. If she decides to offload, then it's fine to listen, even offer some neutral advice. I often told my MB how impressive she was keeping everything together. Whatever you do, DO NOT join in with DB bashing. They might get back together and then you'll surely be sacked as part of the "new start".
MB will lean on you more as she'll need more support. This can be good, and will probably bring you closer. I made sure mine had a supper cooking for when she came home, even if it was just a baked potato in the oven.
Remember to look after yourself. It's a fallacy to "stay for the kids" as they have two parents who are looking out for their best interests. Separations and bumps in the road are all part of life. Remember to look after yourself and be the best nanny you can. Don't stay longer in the job than you need/want to because you feel that the kids need you.
Long post, but I've lived it recently and am aware of the pitfalls! I was live-in so it was all more intense, and we moved house twice during all of this (to a smaller house each time) so disruptive for me too.
Good luck, sounds like you care, and that's a great start.