I know one thing. If I wanted advice from Mumsnet about my MiL I'd substitute her identify for that of another family member. The responses you'd get would doubtless be a lot more measured and less prickly.
The MiL/DiL relationship seems very incendiary. As far as I can see this tends to boil down to competition (she sees her daughter's children more often than her son's, or DiL wants her children to spend more time with her family than her DH.
Unfairly, MiL is sometimes seen to be transgressing boundaries when they are set at Fort Knox height for her whilst remaining at box-hedge level for everyone else. By the same token, if issues arise with the relationship MiLs will usually see DiL as the sources of problem, rather than examining their own relationship with their sons.
On Mumsnet the stock response is that MiLs are hated, and DiLs should just put up with whatever behaviour their MiLs care to dish out.
As far as this thread's concerned, yes, the copycat stuff is childish. But when someone keeps up this low-level antagonism for years on end I can see how it would become very wearing. The trouble with this brand of passive aggression is that if you challenge it, she'll deploy plausible deniability and you'll look unhinged (this is the PA's get-out clause, frustrating though that is). The only thing you can really do is protect your own wellbeing by deciding where your level of contact should lie (because she won't stop). Then stick with that.