2D & 1N b/w Lahore and Multan

Yeah you 'll miss a lot if you don't stop over at Harappa archaeology site.Stay in Sahiwal city for overnight because no option for accommodations in Harrapa city.

Be aware that if driving from Lahore to Multan and if you are of non-south Asian appearance, you'll almost certainly be followed / stopped by the police / Federal Investigation Agency. This happened twice to two separate friends who tried in 2011.

Multan / southern Punjab is considered dodgy by the authorities and they may insist that you arrange your visit with the local (Multan) police or similar. Theoretically there should be nothing stopping you driving down there (as a tourist you shouldn't need a No Objection Certificate) but be warned. You may want to try and call someone official in Multan and let them know your plans.

On a lighter note en route to Multan you could visit the Pakistan Museum of Puppetry in the southern suburbs of Lahore (a google search should bring up the details).

When you say 'shrines', what do you have in mind, exactly?

You do not need to stay in Harrappa, you can do the harappa site trip in a day trip starting from Lahore and ending in Mutltan or vice versa, not much taking time to cover all places to see there.