When I open a LAN world and I have 2 accounts on it on the same computer, the account who opened the LAN had a Steve / Alex Skin

Put the summary of the bug you're having here

What I expected to happen was...:
The Player skins would show up like they should

What actually happened was...:
The player who opened the world had Alex / Steve depending on when the account was created

Steps to Reproduce:
1.Have 2 Minecraft windows open on the same computer with different accounts on each
2. Use one to make a LAN world and play on it with another and look at the Skins
3. e.g. Notch opens two Minecraft windows on his CPU, with 1 window Dinnerbone and the other with Notch's account. Notch opens a LAN world
and has Dinnerbone join it. On the Minecraft window with Notch's account, everything looks fine, On the Minecraft window with Dinnerbone's account it will look like Notch has a Steve skin (Or Alex)