I just want to step back from the tactical questions about the application process and deadlines or the attempts to discern any tiny marginal differences between one law school “feeder” vs. another to reflect on this point:
The OP was admitted to Princeton. F@#$ing Princeton! Arguably the best overall university in the U.S….
…yet their mom thinks that is inadequate.
My God, why do people do this to these poor kids?!
For all of Harvard, Yale, and Princeton, it basically amounts to not being able to apply early, binding or not binding, to any other US private college, and also not being able to apply binding anywhere else. But if it is a public, service academy, or non-US college, you can apply early, rolling, whatever as long as it is not binding.
There is actually some evidence that starting in STEM majors generally is not such a good idea. It is unclear whether or not top law schools really fully adjust for the different grading standards often found in STEM classes, particularly in cases where you might start in a STEM major but then switch out at some point if it is not going so well. Of course a lot of successful STEM majors do well on the LSAT, so it is hard to disentangle.
But yes, the fewer hard-for-you courses you are required to take, probably the better. For many future law students those hard-for-them classes will be required STEM classes. And actually, I would question a STEM student who found college reading/writing courses to be hard-for-them going to law school at all. It is going to be a whole lot of that.
MIT used to post detailed admissions stats to law schools. It was clear when comparing the results to those published by other sources that law school adcom’s understood MIT’s grading system, understood the difficulty of the core, and that MIT students with lower GPA’s than “peer schools” were being admitted to “tough admit” law schools.
Admittedly a small sample size which MIT noted… but the year to year trends seemed clear- for MIT grads, LSAT scores were extremely meaningful and GPA’s much less so. Even at the law schools which are rumored not to be “friendly” to “splitters”.
I have no idea whether this extends to other colleges with an extensive and difficult core… but since someone upthread mentioned MIT…
Please keep the focus on OP. Discussions on the rules of REA should be taken to PM or to a new thread. Likewise the back and forth about MIT and any other school the OP has not mentioned. Thank you for your understanding.
As I recall (and it has been a while) the MIT law school applicant pool skewed to really high LSATs, so it was unclear exactly how MIT grades were being treated independent of the LSAT effect.
That said, I think it is certainly plausible that an MIT applicant might be in better shape than someone who, say, started off in a difficult STEM major at a non-tech-specific college and then switched to something different after not-so-great grades.
Anyway, the OP is looking at Princeton versus (hypothetically) Yale and Harvard. And while this is a bit of a tangent, it is fleshing out a concept referenced above. Among those colleges, Princeton has a reputation for having a relatively high percentage of STEM majors, who tend to average lower GPA. That may make no difference to their law school prospects, or it might have at least some sort of subtle effect. But either way, you could moot that issue simply by not starting as a STEM major at Princeton.
Especially since even with those many STEM majors the average GPA is about 3.7. So for SPIA majors… 
Even if she went to Yale or Harvard, she would still have to apply to the law school. You don’t get special treatment in that process because you attended that school as an undergrad.
Anyone else think the mom just wants to be able to tell her friends that her kid got into these schools and turned them down?
Go to your #1 choice - Princeton!
The first time I heard that concept I thought it must be a joke, and then I started encountering people (online) who actually seemed to have that mindset. Supposedly some people have refused to withdraw applications after being admitted ED not because they don’t intend to go to the ED college, they just want to be admitted other places too for bragging rights.
In this case, the OP would not be violating an agreement, and so it is fine to continue applications for any sort of legitimate purpose. But I agree it would not be cool if the mom’s actual purpose was something like the above.
I’m choosing to believe the mom’s intentions are pure, just misguided.
No, I think the OP is describing the mom’s motivations and biases, and the context from which they derive. I am concerned that a process that will result in such a big, four-year-plus personal and financial investment is being influenced by hunches and inferences derived from a poor understanding of the higher ed landscape in the U.S., though.
I am also worried about the emotional toll of effectively being told Princeton isn’t an appropriate or adequate(!) college choice, despite all evidence to the contrary. That kind of pressure is very, very unhealthy, especially when this student should be given the space and support to celebrate their achievement. I am saddened and gobsmacked all at once.
Let us not start proposing “solutions” that will cause more family conflict, and stop trying to psychoanalyze the parents of the OP. Let us keep to solutions and advice that will make the situation better.
People would like to believe this, but it is demonstrably wrong. Yale stopped publishing the numbers, but the last time showed that 11% of YLS students came from Yale. Another 10% came from Harvard. About 5% graduated from Princeton. To give it some context, only 3.5% of the school was made up of Big Ten (14 schools) graduates.
Of course, we don’t know how much of that is selection effect (i.e. that Yale, Harvard, and Princeton undergraduate have pre-selected a high concentration of students who will have high GPA and test scores and desire to attend Yale Law School) and how much of that is treatment effect (i.e. that Yale Law School favors applicants from Yale, Harvard, and Princeton over similarly accomplished applicants from other schools).
Why not just apply to Harvard & Yale ? Chance of being accepted to either is quite low. If accepted to either or both, then visit each school before deciding. Simple as that.
As far as I can tell…the poster has two options.
1.discuss why she doesn’t want to apply to Harvard and Yale, and the mom agrees.
And in both situations, the student can still choose Princeton as the place to matriculate.
I know my answer is that being done with all this as of now sounds glorious, and I am only a parent!
Further emphasizing MWolf’s post above… please remember this is not a conversation among “friends”. This thread should be focused on helping a high school student (a highly accomplished student!) navigate a challenging family situation. Please keep that in mind in all further posts. (Posts edited that did not comply with the mod directive.)