Grandma spoilers, don't look.
[SPOILER]There are several ways to deal with her, so she never gives you problems, you can give here very strong alcohol (not beer or wine), there is a ring that will cause her to think your a .... (sorry can't spoil that one.
You get an item from a minigame that you need to give to helpful person in the Temple District (not an indoor person).
Additionally as mentioned you can give her gloves, but alot is random, so it's just such a huge pain in the ass, unless you have the booze or ring.
Oddly enough if you like to be efficient with your time and don't go in the detectives office (auto kicks you out of office at 12am, so you lose the whole day) till 11pm, you can spend the whole extra day, doing quest and she lets you in the house without even asking anything, until you start the investigation.
Trust me, most of the names I have been called you can't translate in any language...they're not even real words as much as a succession of violent images.