Hmm, something is unclear to me. You wrote that unetbootin offered to choose the maximum amount of RAM for the system. I've never seen that.
The only slider I know of is for adding a persistency file where the system can save changes you make during the live-session, like adding an application (LibreOffice?) and have that available on the next boot. However the flashdrive is formatted as FAT32 and that has a filesize limit of 4GB, so you can't use the maximum free space on the drive.
You have to realize that the running system is in fact a compressed Read-Only file on the flashdrive and the extra information and programs are stored in an other compressed Read-Write file on the flashdrive. That is like running from to different drives. During a session all you make it do is stored in your 2GB computer memory, there is no Swap it can use to dump stuff temporariliy. The system might use some 250 MB, but a browser alone with a few tabs eats easily > 1GB. So your computer will very soon be overloaded, explaining the severe lagging. None of this will happen once the system is installed to your eMMC. But I'm not too sure a dual boot (Windows/Linux) will be possible on your 32GB drive.
Hope this helps.