If Margret refuses to speak or is dead, you have a slightly different task: getting into her room in the Inn. Unfortunately, lockpicking skills aren’t allowed to suffice here- you need the key to her room. You have, thankfully, several options here.
If Margret is alive, she may have a copy of the key. Strangely, if she dies out in the marketplace she may not have a key on her, but if she is in the Inn, she does have one. This is a strong test of your sneaking and pickpocketing skills, as she stays in the open when in the inn most of the time, making it hard to sneak up on her without someone else spotting you.
If Margret is dead or you want to try something slightly less difficult, you can hide yourself behind the counter- while it is open on the side towards the fireplace, only rarely do the patrons look at it from there, and the innkeeper rarely turns from the front door. A copy of her key is frequently on one of the shelves under the counter, so if you can snag that you should be alright.
Oddly, if you enter the Inn and best Cosnach in a fistfight so that he befriends you, you may become able to take things from around the Silver-Blood Inn without it counting as stealing. If this occurs, you might be able to simply walk up behind the counter and take the key with no issue. While it is a glitch, it does present a nice alternative for those who are less inclined to sneakery and don’t want to spend ten minutes saving and reloading until they can successfully pilfer the key.
Once you’re into Margret’s room at the Inn, you’ll need to look around for her journal- on finding it, you will need to open it. While you don’t have to actually turn the pages or take it to read it and get the information for Eltrys, it does help to provide a little insight. According to the journal, Margret arrived with the intent to investigate the Silver-Bloods, and obtaining the deed to the mine only became an issue after she’d been present for a few days. According to the journal, Thonar Silver-Blood calls pretty much all the shots for the whole family, and is thus the most likely person to have either the deed or information relating to the mine specifically. She has- or had- been becoming a bit wary lately, as there were hints that someone was observing her.