Dog disobedience?

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Hey guys, I have a question about my mom's dog, who I occasionally have to take care of.

Whenever my mom has me take care of her dog, he gets really bad separation anxiety and will try to run outside to chase after her car whenever she leaves, and will wait by the door for pretty much any chance to run outside, whenever I'm the one taking care of him.

He's usually a pretty obedient dog, and over time he's grown more accustomed to my commands, even when my mom is gone.

For example, if he runs outside to go after my mom, I'll call him back and sometimes he does actually come back. But other times he'll just stop dead in his tracks but won't come back and basically just sits there, like he's conflicted as to what he wants to do. In the beginning, he wouldn't listen to me at all.

More recently he's started a new behavior where if I tell him to stop and come back, he stops, but then he rolls onto his back and exposes his belly to me. It's like a 50/50 chance as to whether he'll listen to me and come back or do the belly-up gesture.

Is the belly exposure a sign that he is being submissive, or aggressive and resistant to my orders?

Also, how do I get him to be more compliant with my commands?