Today ALL Americans pay less for all services because indirectly all services compete with services illegal alien perform (vegetables, restaurants, any place that gets cleaned at night). Some people chose to ignore that EVERYONE including themselves is part of this very very large necessary economy.

Illegal aliens come in because the USA needs them. As the population ages this need for young aliens will become larger and larger. An economy has to have balance and today there is an imbalance [young versus old people] that illegal aliens only begin to fill. Today there is no realistic mechanism for these people that are needed and are good for the USA economy to come in.

Making aliens legal brings them into our tax system, increases their wages, and more fundamentally brings young people into our economic system that are and will more and more be fundamentally needed.

p.s. Back to the OPs question. The nanny can easily and with no hassle at all travel withing the United States. She can advertise she is illegal. No one will care. As far as Puerto Rico is concerned, it is not the United States. You have a strong chance of having problems.