Oooooh, that'a a tough one indeed. I'm a dirty smoker, and I'm extremely paranoid about it. I'd never smoke indoors anywhere, ever, under any circumstances because that's gross (although I do smoke in my car on long trips - with the windows wide open of course), and I am horrified at the thought of others smelling smoke on me, annoying others with the smell or the smoke, or in some cases of people even knowing that I smoke. And I especially try very hard to never go around children when I would smell of smoke.
If I have been smoking and I find myself around children, I will go to the toilet and very thoroughly wash my hands, arms, and face (luckily I don't wear make up); add some lightly scented lotion or very mild scent spray (not perfume as I find that only makes it worse); lightly spritz my hair with the spray as well; and then I'll try to change shirts if at all possible or at least remove my cardi. If I go on a long drive where I know I'll be smoking, like when I go to visit my sister and her DC a couple hours away, I'll set off in an ugly old shirt, with the top I intend to wear for the visit in the trunk, and I'll change when, or just before, I arrive. I haven't had any complaints, and my sister for one absolutely would not hold back if I smelt of smoke and tried holding her infant, so I think my method works fairly well!
Could you ask your nanny to do something like that ^^ before she comes in to be with your DC? If you don't want to outright sack her right away, perhaps tell her that you don't want to dictate what she does outside work hours, but since it is affecting you, your home, and your children, could she please consider smoking outdoors, and then when she arrives to work please try changing clothes, washing her hands and arms and face, and maybe also carrying some lightly scented lotion or spray to add after washing? You could ask her to do that, give it a trial run, and then revisit the issue or even let her go if that doesn't work and the smell is still bad.
And, holy hell, she really needs to stop smoking in an enclosed environment!! If her smoking is affecting the smell inside your home, she is definitely doing it wrong!! She should only smoke OUTDOORS FFS, and at least roll down the bloody windows if she's smoking in the car - especially if she is hanging out with children - because no person should ever smell so strongly of smoke that it lingers after them when they leave! She must be absolutely wallowing in smoke with zero ventilation if it's that bad!! Bloody hell!
BTW - I think you definitely should demand that she not smoke in front of or around your children, if you have not told her that already.