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 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.

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.

Arnold Schwarzenegger rocked his wedding ring out in public during the holidays  -- another sign that his marriage to Maria Shriver ain't as dead as it once seemed.

TMZ broke the story ... Maria has been having second thoughts about pulling the plug on the marriage -- despite Arnie knocking up the family maid -- because of her deeply held religious views.

Arnold hadn't been photographed in his wedding band in months, but over the past few days -- Arnold dusted off the ol' ring and reminded the world he's STILL a married man.

We're told Arnold was vacationing with his sons -- but it's unclear if Maria was there too.

Maria Shriver is telling friends she's now unsure if she wants to divorce Arnold Schwarzenegger ... TMZ has learned.

We're told Maria is torn, partly because of her strong religious beliefs that do not include divorce. 

Making matters even more complicated -- we're told Arnold still desperately wants Maria back, and has been "extremely sweet" to her and has made numerous gestures -- which include presents -- to win Maria back.
 
Maria filed for divorce on July 1, though she moved out months earlier.  She's already bought a mansion in Brentwood, CA, which she's in the process of renovating.

Arnold Schwarzenegger took a nice gander at soon-to-be ex-wife Maria Shriver today as they went in to church in Santa Monica, CA.

Hallelujah.

The Shriver/Schwarzenegger family driving misery continued yesterday when Maria Shriver got a parking ticket in Brentwood ... which our camera guy politely handed to her before she drove off!

Her son Patrick was pulled over for speeding last week, Arnold got a parking ticket the day after he left office, and Maria had a slew of parking and driving woes in 2009 (see below) that we thought were behind her.

Guess not.

Arnold Schwarzenegger's aspiring-model son Patrick earned the Schwarzenegger family yet another traffic ticket -- after the 18-year-old was cited for speeding in Santa Monica.

Law enforcement sources tell TMZ, Patrick was pulled over last week in Ahnald's 2009 black Audi after going 54 mph in a 35mph zone.

We're told Patrick was cited for the violation -- and sent away without further incident.

Like father, like son.

Arnold Schwarzenegger and Maria Shriver broke bread last night -- their second meal together in less than a week -- but this dinner date was about more than just a meal.

Arnold and Maria went to Mastro's Steakhouse in Bev Hills with their kids ... Patrick, Christina, and Chris ... to celebrate Chris' 14th birthday.

Every celeb in town knows Mastro's is a paparazzi hotbed -- so, it sure seems like the Schwarzeneggers wanted to put on a show for the cameras.

The message: We can all get along ... for good steak, at least.