Elliott's mother, Mary, better known as Mom, is having a bit of a rough go. Her husband has recently headed south to Mexico (which, BTW, he doesn't even like) with another woman, and she's been left to raise her children solo. Also? One of them is hiding an alien in his closet… so there's that, too. Overall, Mary's doing the best she can, but she's a pretty ineffectual mom.
Mary's children don't take her very seriously. Gertie calls her by her first name. Elliott has no reservations about bringing up her absent husband at the dinner table, throwing shade at her Halloween costume, or defying the curfew she set for him. Even Michael's friends get in on the act, as demonstrated in the game night scene when they're smoking in her kitchen and ordering a pizza without her consent.
Tyler is especially disrespectful, first pretending like he's going to grab her rear end and then calling Elliott a d-bag right in front of her. Sure, Tyler's belittling Elliott, but the fact that he'll level such an insult right in front of Mary shows that he doesn't have a lot of regard for her, either. That Tyler's a real class act.
Look Alive, Mary
As the head of the household, she's disengaged. This is played to slightly comic effect when she returns home with groceries and dry-cleaning, just before Elliott's school calls to say he was hammered in science class. E.T. is freely walking about the house, but she doesn't notice him.
Moments later, when Gertie proudly proclaims that E.T. can talk, Mom replies, "Of course he can talk," thinking that Gertie's referring to someone other than the hung-over alien in the bathrobe ambling around her living room. Mary is portrayed as harried and distracted.
Later in the film, the kids are able to sneak E.T. right past her on Halloween by pretending that he's Gertie dressed as a ghost, even though E.T. and Gertie have totally different body types, definitely don't move the same way, and Gertie's previously expressed her excitement over her super-cool cowgirl costume. Good eye, Mary.
Mama Bear in Training
There are moments when Mary steps up her mom game, though. When she first meets E.T. in the bathroom, she views him as a threat, and removes her children. She's wrong about E.T., of course, but her instincts to protect her children are on point.
Similarly, when federal agents storm the house moments later like menacing space zombies, she goes into mama bear mode again, gathers her kids, and screams, "This is my home!" She may not be the most effective leader, but she does want to defend her family.
She even comes around on E.T. When the doctors pronounce him dead, and Gertie wishes for E.T. to come back, Mom says that she does, too, showing that she no longer sees E.T. as a threat, and has come to value and trust her kids' input. Mary may not win any "Mother of the Year" awards, but she's trying.