Interrupt the two of them

You get up and walk over to the restrooms, approaching Alice. You wrap your arm around her waist, and say, "I have the picnic stuff ready, baby. You hungry?"

She looks at you, back to the man, and pats you on the chest. "Sure, baby, let's eat". She looks at the man and says, "it was nice meeting you, have fun with your family!"

The man smiles and nods, and says, "you too, enjoy your picnic!"

Alice allows you to lead her away and back to the picnic table. She looks at you and says, "he was actually really nice, he was here with his wife and son having a family picnic, too. I bumped into him coming out of the restroom, and noticed he had one of those smart watches you keep talking about getting..."

You take the direct approach with her. "That seemed awfully friendly for asking about a watch..."

"I...you didn't think I was flirting, did you? No baby, not at all," she tries to reassure you, but you know her body language too well. "He was married and had a kid, they're right over there!" she points to the playground, where you see the man with a woman and a kid, playing together.

You say, "Alice, I saw you from across the park, you were definitely putting off signals. Astronauts could have seen you were flirting with him."

She huffs. "Fine," she admits, "maybe a little. But it was just in good fun, everyone flirts. You're not jealous, are you?"

"I...not really," you admit. "I've just never seen you flirt with anyone else, and it was a shock. I'm sorry if I overreacted."

She smiles at you and sits down as you lead her to the table. "I understand, baby. I'm sorry if I upset you, let's eat, okay?"

The two of you sit down and eat, forgetting the minor incident. During dinner, she does mention she found out a few things about the smartwatch you wanted from the man, and actually got a suggestion from him about another watch you might like better. That she was still thinking about it doesn't make you feel any better, but on the other hand, the suggestion about the other smartwatch might actually be good.

You finish dinner, pack up, and leave the park. You got home earlier than expected, and you decide to take a long shower and watch television with Alice for the rest of the night.