You cannot. You only have access to records from your stake. This is a side effect I hadn't considered with the continued increase in YSA stakes. Your other option is to move your records back to your family ward, but that may not be what you want to do if your choice is to serve and be involved in the YSA stake.
By your comment, I'm assuming you're a YSA and not serving in a leadership capacity in the YSA stake. If that was the case, you should have an out-of-unit record that gives you access to both stakes. That brings an interesting consideration: If you're serving in a calling in your parents' ward/stake, maybe they can create an out-of-unit record for you to access records in your parents' ward/stake. I have certainly seen cases where YSA serve in other capacities besides their singles ward. For example, I have a family member in a YSA ward who is in the stake YW presidency (but the YSA ward is part of a conventional "family" stake).
I suggest having one of your parents print out a ward directory for you. You get a PDF, so if electronic is easier than paper, that would work for you.