Is it in any way possible for me to add two poll widgets to the sidebar of my forum? I have two polls that go on every two weeks and I'd like them to both be on the home page.

Well, you would probably have to create a poll using a poll host, such as poll daddy and add their codes into a custom widget.

Well, ideally I'd like to be able to reference two polls from my forum, on the home page, so a poll host wouldn't work. If I used a poll host, it wouldn't update the original poll post.

If there were some way that I could get the html code from the poll widgets that are provided, I could easily pull this off.

Probably, host polls on another site. Get embeddable codes from that site, add it in different widgets.

Good idea!