I have to agree with the people that say Dave was in the wrong on this. He probably wasn't being at all malicious about it (never attribute to malice what could just as easily be explained by ignorance, right?), but that doesn't change the fact that his being in her house was IMO completely, undeniably wrong if not rude on top of that.
Dave just had his own celebration with her. He knew that his wife wouldn't want him at this party (and I'm fairly certain that he definitely knew. I find it extremely unlikely that after the two of them making a point to not socialize or celebrate anything together for either children for HALF A DECADE that he wouldn't know she wouldn't want him there. This cannot have been the first time something came up where the child wanted both parents at their celebration. Actually, it's possible that Pam asked her father because she knew her mother would say no if SHE asked. She is 11 after all, not 4, and thus more than old enough to consider playing her parents...not that I'm talking from experience or anything...).
And, birthday or not, Pam is not so young that she can't be made to handle disappointment. Because the parties (two of them) are GIFTS. She is not entitled to have both of her parents there. This isn't a wedding or the birth of a child or something where it is a once in a lifetime event where she deeply, truly needs them both there. She may feel like it is at the time, but it's not. She has two parents that seem more than happy to lavish her with love and attention. Just not together. And that has to count for a lot. Because, where they are right now, what was the point of having him there? He wasn't involved or engaged. Her mother might have been a bit noticably uncomfortable than she would be otherwise, so I can't imagine she was quite as fun as she could be.
All of that said, he decides to go into her house and STAY there without her permission. This is the first time he was ever been inside her house and it's without permission when he already must have known he wouldn't want him in there? And browsing? That's kind of weird. Because even though he was once her husband and is her children's father, this man has been essentially demoted to 'acquaintance' status. Someone you see occasionally but is not, in any way, close enough for it to be okay to make himself at home at your house. They are not friends, they are not family (not hers anyway) and no one (especially not a child) has the authority to issue an invitation to her home. I don't know if inviting people over is normally a thing that Linda lets Pam do, but I doubt it. And if Dave didn't feel comfortable outside, he could have made his excuses and left. Surely he had something to do with his time since he had not planned to be at the party to begin with.
I think Linda did a pretty decent job handling a weird situation. Though I do think she would have been entirely justified in doing something, anything, to usher Dave out of her house ("Oh, we're starting the Game of Great Excitement! Why don't you go over to Pam and help her out?") if not off her property.