lightbrite: An engagement ring has no significance in Judaism. So inheriting an engagement ring from a family member who got divorced and/or had an unhappy marriage would be no different than inheriting a car or chandelier from a family member who got divorced and/or had an unhappy marriage.
(A wedding ring does have religious significance so my above point wouldn’t be applicable to it.)
Regarding naming someone after someone who died young, I understand people often add an additional name to the person being named after, but it definitely is done to name people after people who passed away young.