If both machines are XP - then they should be defaulting to simplified sharing - which doesn't need passwords. If this is disabled, you need both machines to have the user id/password used to log on to other machine set up as a user on them (ie, both machines have same users set up). If the network connection is dropping, there may be something wrong with one of its components (you should not need to run the network wizard, once network has been set up). With ICS running, internet connected machine is acting as DHCP server - so laptop should be set to pick up IP address automatically. I think there is a policy which can be enabled which will drop a network connection after its been idle for so long - but unless you've been playing with policies (run gpedit.msc), this shouldn't be set.
What you've got sounds basically ok - but if you can give examples of when network connection gets dropped (unless its entirely random) - eg, after so much time, often when running this app, connecting to this site etc, you may get some better advice (there are many members here with extensive - better than mine! - networking experience).