My first piece of advice is for your sister to stop
correcting her mother in law - cold turkey.
A daughter in law's conversation with her mother in
law should be strictly limited to compliments.
Secondly, both halachik scenarios you
described may have specific heterim depending on various particulars. Perhaps a
review of the halachos with a knowledgeable Rav may help your sister determine
what is considered a chumra or a minhag rather than a full blown issur . Don't
allow a chumra get in the way of a perfectly fine relationship, or worse, a
perfectly fine cholent
My advice in this particular circumstance would be
for your sister to talk to her husband - the son; explain to him what
she has witnessed and see if he can straighten it out. This will of course
depend upon the son's relationship with his Mom.
Better yet, I would have the son, her husband, talk
to his father and have his father point out the various halachos to his wife.
If this does not clear up the situation I would
advise both your sister and your brother in law to seek a knowledgeable and
experienced Rav TOGETHER and discuss the particulars with
him. The Rav should be able to advise the couple as to what the
Torah requires of them.
Hope this helps!