Are there sources that say women do not have to cover elbows? Because I've seen Orthodox women not covering them and I want to be able to say that there are sources that support their actions.
The best development I've seen on this is Rabbi Yehuda Herzl Henkin's Contemporary Tseni'ut. It appeared in Tradition 37:3 (2003), as well as its own book. The Tradition article is available online, paid subscription required. Here's his conclusion, as relates to your question:
It emerges from Rashi, Yerushalmi and Korban ha-Eda that peritsut in exposure of the upper arms comes not from the arms themselves, but from the body being visible via the arms; this, then, is what Sefer Rokeah means by zero’oteha megulot, the same language as zero’oteha halutsot in the Yerushalmi. This is a powerful source for limmud zekhut in behalf of otherwise modest women whose sleeves do not reach to their elbows.
A typology can be established, then, as follows:
1. sleeveless dresses—forbidden by all opinions, as body can be seen.
2. short sleeves, loose—forbidden by all opinions if body can be seen.
3. short sleeves, tight—body cannot be seen, but forbidden if most of the upper arm is uncovered (rubo ke-kulo)
4. sleeves half-way to elbow—forbidden because of tefah meguleh, room for limmud zekhut
5. sleeves to within a tefah of the elbow—minimum permitted
6. sleeves to elbow—recommended
7. sleeves to below elbow—first level humra
8. sleeves to wrists—second level humra.
This does not supplant any communal or familial minhag.