What is the nature of the tension regarding Mrs. Van Daan's inappropriate actions toward Mr. Frank? How is it resolved?

The tension begins in act 1, scene 3 when Mrs. Van Daan asks Mr. Frank to take Peter on as a pupil. Mr. Frank defers to Mr. Van Daan, but Mr. Van Daan says that Peter won't listen to him, so he is welcome to it. When he  agrees to teach Peter, Mrs. Van Daan kisses Mr. Frank and says the following:

"You're an angel, Mr. Frank. An angel. I don't know why I didn't...

The tension begins in act 1, scene 3 when Mrs. Van Daan asks Mr. Frank to take Peter on as a pupil. Mr. Frank defers to Mr. Van Daan, but Mr. Van Daan says that Peter won't listen to him, so he is welcome to it. When he  agrees to teach Peter, Mrs. Van Daan kisses Mr. Frank and says the following:

"You're an angel, Mr. Frank. An angel. I don't know why I didn't meet you before I met that one there. Here, sit down, Mr. Frank . . . (She forces him down on the couch beside PETER.) Now, Peter, you listen to Mr. Frank."

The stage directions after Mrs. Van Daan's flirtatious advances say that as Mr. Frank goes to teach Peter in another room, Mrs. Frank stops her husband and wipes off the lipstick mark that Mrs. Van Daan left on his lips. Mrs. Frank never says anything directly to Mrs. Van Daan about the kiss or inappropriate flirting. Mrs. Frank refuses to lower herself to Mrs. Van Daan's childish ways and she won't give Mrs. Van Daan the satisfaction of knowing that it bothers her. Mr. Frank also never encourages Mrs. Van Daan, nor does he respond to her advances, which helps to keep Mrs. Frank feeling secure within her marriage. 

The only time that Mrs. Frank loses her temper is when she discovers Mr. Van Daan has been stealing food during the night. She never turns her anger to addressing Mrs. Van Daan's flirting, though. Therefore, the resolution is that Mr. and Mrs. Frank do not give Mrs. Van Daan the attention she desires. To them, discussing the issue is beneath them and not worth the energy to try to stop Mrs. Van Daan from flirting. Plus, Mrs. Van Daan becomes very riled up in an argument, so the issue isn't worth addressing. If Mrs. Van Daan's flirting had become more of a problem, they would have addressed it. As it stands, Mrs. Van Daan never crosses too many lines to spark any real debate or argument on the matter. Anne says the following at the end of act 1, scene 3:

"To pause for a moment on the subject of Mrs. Van Daan. I must tell you that her attempts to flirt with Father are getting her nowhere. Pim, thank goodness, won't play."