One useful way to connect both of these texts is through the principal theme of disillusionment and how it is explored in the case of both of the central characters depicted in these stories. For example, Leila, having had such high hopes of her first ball and eagerly anticipating what it would be like, has her dreams of perfection and beauty cruelly punctured by the fat man who insists upon dancing with her. He paints a grim and vicious picture of her future:
And these pretty arms will have turned into little short fat ones, and you'll beat time with such a different kind of fan--a black ebony one... And your heart will ache, ache...
Leila is confronted with the brevity of youth, and as a result wishes that the "little girl" inside of her could throw "her pinafore over her head" and sob. However, swiftly, Leila once again loses herself in the joy and beauty of the ball and forgets the injection of grim reality that he brings to the story. The story ends with her moving on so completely that she fails to even recognise the man that had upset her so strongly.
By contrast, in "My Greatest Ambition," the protagonist dreams of nothing else than being a comic strip artist, and is filled with joy when Boy Magazine accepts his first submission. However he quickly realises that he is being unrealistic and that this does not mean that his future is guaranteed. By the end of the story he is forced to realise that his "greatest ambition" that was such an integral part of his life has been shelved and he has moved on:
The only thing that was ever real to me I had "grown out of." I had become, like everyone else, a dreamer.
Both protagonists therefore face disillusionment and reality, but how they respond to it is very different. For Leila, she is able to put it to one side and ignore it for a little while longer as she enjoys her first ball. For the protagonist in "My Greatest Ambition," his courting of reality leads him to put to one side an integral part of his life and we feel, as he undoubtedly does, that this involves an acceptance of something that is only second best that will leave him unfulfilled.
I have included a link below to give you more information on "Her First Ball," but unfortunately there is not a similar link to "My Greatest Ambition." I hope this helps.