Ok so I had to start a new game because of too many bugs in my old one. Well I married Ysolda this time around because Aela just complains about every other house. Granted it shows she cares about the kids but whatever. Anyway so since I don't have my own house yet I am living in her house. I stuffed some superfluous gear and miscellaneous in her chest. Does it reset? And if so how long do I have until it resets?
Normally, spouse property does not respawn. However, UESP claims that Ysolda's house respawns after ten days even if you marry her:
If you chose to live here after marriage, sleeping in the single bed will still give you your Lover's Comfort resting bonus, but the house does respawn after ten days.
Note that some kinds of containers never respawn, even if the location around them does respawn. If you can find such a container anywhere in the world, including in Ysolda's house, you should (in theory, I have not tested this) be able to store things there indefinitely.
Being married to Ysolda, I can assure you that the chest does not reset, and there is almost no chance that your items will disappear. Your items will not be stolen nor gone due to respawning. I lived in Ysolda's house for a while before I bought breezehome and I left most of my armour/weapons that I was lugging around. Hope that helped :D