Taxi would probably be the fastest at around 30 mins/$45. They will be plentful around US. The CTA Blue Line from Clinton would take about 45 mins and cost $2.25.

Taxi will probably your best bet especially when it's Sunday afternoon, but it will be expensive.

The L train will probably get you there at the same time but you will need to walk about 2 city blocks to the nearest blue line station. Don't know your luggage situation so I can't tell you if it's worth the trouble but it will be definitely much cheaper.

My advice would be to take the #351 out of Ann Arbor at 7:26AM.
Stash you bag in the locker at Union Station and go have lunch.
Get your bag and then ride the blue line out to the airport before 2PM.
Never assume that Amtrak will get you to CHI at 4PM even on Sunday.

Thanks for the helpful replies - the reason I'm cutting it close with an afternoon return to Chicago is that I have a morning visit with my AA uncle planned - so that brings up the timeliness of Amtrak - can anyone tell me if the train is likely to be close to on time or might it run late into Chicago?

There is a 33% chance that it will be on time to Chicago based on the 12 month and January figures. Amtrak does not say how late the other 67% of Michigan Service trains are.
The bulk of the delays are blamed on Norfolk Southern and not Amtrak.
The OTP for Amtrak trains are posted under "Routes" on the Amtrak website.

IMO...I would never attempt this.

Seems to me that you've DECIDED to take that particular train. Now that you know the OPTIONS of getting out to the airport I would WAIT until you arrive in Chicago and then decide the best way to get to the airport. You know the taxi will be faster and more expensive and if you don't have a lot of time to spare that becomes the "obvious choice" (to quote a long-time Fodorite).

I took the early morning train (the 7:26am) from AA and it was late by 1.5 hours, so I didn't get to chicago until shortly before 2pm.

If you're going to attempt this I would check in online and be prepared to carry on your luggage.

The blue Line will take exactly (if no incident) 45 minutes from Clark and Lake (i just hop on the quincy orange line and take it to Clark line blue line because I'm lazy like that.)

Its' a gamble though because for Ohare you definitely need at least 1 hour to get through security etc. etc. Again depends on your luggage situation because if you need to check luggage I really wouldn't suggest it.

I would check your airline's policy on missing flights. It might be worth it to just pay the fee (when you miss the plane) and get on the next flight. Which is the most expensive out of all your options, but that's only worse case scenario.

Just a question, but why are you taking the train rather than either flying Detroit/SF or at least Detroit/ORD?

Having lived around there most of my life, the train route is not that scenic, slower and probably costs at least as much as a plane.

But to answer your question, take a cab.

Also, why not rent a car and drive it? Google tells me you could drive AA to ORD in under 4 hours. On Sunday, traffic wouldn't be bad, and it's a pretty straight shot on expressways. You would even have enough time to take US 12, which offers a marginally more scenic route than I94.