Arnold Schwarzenegger spent Mother's Day with the mother of most of his children ... showing up at Maria Shriver's new Brentwood home yesterday.

Our sources say the day went well, but as for reconciliation ... even though Maria has gone back and forth on it, the divorce is still all systems go.

Arnold also spent Saturday with the fam ... showing up at his daughter's graduation from USC sporting a new goatee.

Arnold Schwarzenegger showed up to his daughter's graduation from USC yesterday sporting some new facial hair that is clearly not indicative of a mid-life crisis. 

At least it's not a tumor.

Arnold Schwarzenegger was caught red handed speeding through Beverly Hills Wednesday ... BUT the cop let him skate -- 'cause seriously, who challenges The Terminator?

It all went down on the rough streets of Bev Hills ... the ex-Governor put the pedal to the metal of his Mercedes AMG ... then was stopped dead in his tracks by a man in crisp blue.

"The Expendables" actor must have turned on the famous charm that both cops and maids just can't resist -- Arnold got a warning and was sent on his merry way.

Hasta la vista, baby , $400 ticket.

Arnold Schwarzenegger would like Maria Shriver to take him back, but he's not holding out hope and is at peace with the likely end of his marriage ... sources very close to the actor tell TMZ.

As TMZ first reported, Maria has waffled on divorcing her hubby, partly because he still has a strong emotional hold on her and partly because divorce runs counter to her religion. But we're told as time passes and both Arnold and Maria have created separate lives, divorce is looking more certain.

We're told Arnold believes Maria's friends have done everything they can to poison the waters, imploring Maria to stay clear of him.

And our sources say Arnold and Maria are already "very close" in working out a financial settlement.

Whatever they decide, we're told both Arnold and Maria are in lockstep over one thing -- making the break up as painless as possible for their kids.

Patrick Schwarzenegger was treated in an Idaho hospital after injuring himself skiing yesterday ... continuing the Schwarzenegger family tradition of sports injuries.

The 18-year-old son of Arnold Schwarzenegger and Maria Shriver tweeted a few photos after the accident, saying, "Little ski accident today. Some bruises and stiches down back and but. Thanks to sun valley doctors for everything."

The Schwarzeneggers are no strangers to sporting accidents. Christopher Schwarzenegger was in a serious surfing accident last year that landed him in the ICU for several days. The Governator himself broke his leg in Sun Valley as well back in 2006.

More signs Arnold Schwarzenegger and Maria Shriver are reconciling -- they went furniture shopping together yesterday ... FURNITURE SHOPPING!!!

The former couple hit up The Ivy in Santa Monica for a lunch date Tuesday ... and after the meal, they walked over to a nearby furniture store and checked out some of the goods.

Arnold's probably a couch expert by now ... considering he probably slept on one for a while after Maria found out he had a love child with the former maid.

As TMZ previously reported, Maria has been extremely conflicted about going through with the divorce because of her strong religious beliefs ... and we're told she's flip-flopped on the whole divorce thing many times.

One thing is for sure, Maria is the one in the driver's seat.

60 something action stars Arnold Schwarzenegger and Sylvester Stallone both needed surgery after filming "Expendables 2" -- which gave us a great idea for their next blockbuster. Roll it!!

Arnold Schwarzenegger and Sylvester Stallone got his and his shoulder surgeries at a hospital yesterday ... making millions of fans feel sad and old at the same time.

Ahnald posted the pic yesterday ... with the caption, "After all the action, stunts & physical abuse shooting 'The Expendables 2' and 'The Last Stand,' it was time for a little tune up on my shoulder. Look who was coincidentally waiting in line behind me for his shoulder surgery."

He added, "Now we're ready for another round of great times and action when we shoot 'The Tomb.'"

For the record, Arnie is 64 and Stallone is 65 ... and still in better shape than most humans.

Arnold Schwarzenegger went all the way to India this week ... and all he got was a big fat REJECTION from the Taj Mahal.

The ex-Governator -- who's in town for an environmental conference -- was turned away from one of the 7 wonders of the modern world this morning after he informed it was closed to tourists due to Muslim prayer sessions.

According to Ahnald's tour guide, the actor was totally bummed out ... and went down the street to take a few cell phone pics with the building in the background.

Undaunted, Schwarzenegger continued his trek through India ... and took out his frustrations on the biggest piece of naan he could find.

Arnold Schwarzenegger's baby mama, Mildred Patty Banea, is officially a single woman ... nearly four years after she filed for divorce from her husband ... TMZ has learned.

Baena's divorce made the news shortly after it was revealed she had the Governator's love child because her divorce docs stated she and her husband had no minor children. 

Baena originally filed for divorce in February 2008, seeking nothing in support. Finally, on January 3, she filed for a default judgement ... and it was granted that day.

Arnold, of course, is in the middle of his divorce from Maria Shriver. But as TMZ first reported, Shriver has been having second thoughts on pulling the plug and Arnold has recently been spotted wearing his wedding ring.

Maria Shriver sure knows how to ring in the new year  -- just days after Arnold Schwarzenegger wore his wedding ring out in public ... his divorce-shy, estranged wife was sporting something on her wedding ring finger, though it's not clear if it's the real deal.

The photo was snapped today in Beverly Hills -- interesting she wore something on that finger just after we posted the pic of Arnold.

TMZ broke the story ... Maria has been having second thoughts about divorcing Arnold -- despite the whole lovechild thing -- because of her deeply held religious beliefs.