Adelaide knows what the two of them expect now - they expect that she will come with them to the Dog Park, will stay with them from now on. She knows it because it's exactly what she would do, if she was free to do it. If her mind hadn't already jumped ten steps ahead, reasoning out consequences and realizing all the ways everything can and probably will blow up in her face.
She knows she can't stay with them.
She knows she ought to tell them, right here and now.
And she also knows she's going to put off that unpleasantry as long as she damn well can.
They need to go to the Dog Park, to get the meds that Adelaide doesn't actually need, to keep up the ruse of her story now that it's started. She doesn't know where she'll now get what she actually came here for, but that is so far on the back burner that it's hardly an after thought. So she'll go with them to the Dog Park, bask in this not-so-perfect reunion as long as she can, and then she'll tell them it's time to go. Because if she has to look at her brother's Let Down expression for one more second right now she might just shut down.
There has to be a way to resolve this, to be where she wants to be, but she needs time to find it. She can only have faith that the connection between the three of them is strong enough to withstand until she does.
When Sarge joins them with the steaks in tow and they head back out into the glaring sun, Adelaide tries for levity. "Well I don't have the supplies I once had, but I guarantee you'll be firing whatever Hound-person you have chefing for you when you see how I make do," she says, just as confident as ever. They emerge beside the big SUV she drove in, strangely clean and shiny for the surroundings, and she lifts a brow at them both. "I guess I'll follow?"