Been watching this thread since it was first posted and then the comments.

1. OP understands the rules so when his SIL purchased the tickets did he not think to ask/comment about BE to her?
I certainly understand that she (SIL) may be an infrequent traveler but he obviously travels more frequently. My friends and relatives seek my input when they travel as they know there are "tricks and traps". I warn them about BE.

2. I do not think UA is entirely blameless but I certainly understand they probably thought on the first full flight since one child was sitting behind the mother and the other child that someone in that area may have been willing to move and accommodate them once they were on the plane. However, guilting another passenger into a middle seat was not the answer and I really do not understand why the OP was not willing to trade his "good" seat for the middle seat person. Oh it is okay for some else to suffer. Little sympathy. I am sure on the first flight the GA/FA is looking at OP and thinking why are you not steeping up to help swap your seat?

3. Of course it was easier to find three seats together on the second flight - it was not a full flight based on the information provided.

4. Do not agree BE should not be sold to families - for some people that would mean the difference between flying and not flying. BUT the option is there to purchase seats together. Yes, children are important. I have one, but it was my responsibility (when he was little) to ensure he was seated next to me or his father. Sometimes that meant travelling down the back of the plane when I had less money and/or status - as parents that is OUR responsibility.

Like others and I have posted about some of those experiences, I have proactively offered to move for families, but there are other times when I choose not to - my reasons for choosing not to should not need to be explained. You ask, I answer and I will not be guilted into swapping for a worse seat because of your lack of preparedness.

In the original post, the OP could have avoided this angst for his SIL if he:

1. He had an upfront discussion about BE with his SIL;
2. He had given up his better seat for the third person in the row where his SIL was sitting.