Haven't RTFT but I've seen some misconceptions about the Cambridge's nanny.
Yes she's in uniform, the uniform of one of the (maybe the) most prestigious nannying college in the world. The majority of Norlanders would be proud - would actually request - to wear their ceremonial uniform for an event like this.
Why? It's not a company they work for (as a pp said), they work for the Cambridges. The uniform is not some child-care company uniform, it is in fact the equivalent of wearing your graduate gown and cap, or possibly military dress uniform, to a formal occasion.
Many Norlanders won't wear even the day-to-day uniform when out with their charges, in order to blend in and reduce any security risk.
Norland uniforms mark out graduates of a prestigious college. One of the many Norlanders we've had commented that when in ceremonial dress other guests will come and chat to them, because people are interested in the college, training, and its graduates.
I'm not a big royal fan, but it's unfair to criticise them for 'forcing her to look like staff', because that's not what's really happening here.