Well, it's not just that he didn't want kids. It's that in contrast to casey's other guys, Tony refused to allow Caylee to spend the night and thought it was inappropriate for her to be hanging out in his apartment where a bunch of bachelors had sex, drank and smoked pot.
It is relevant because her new relationship occurred right at the same time that her parents were starting to refuse to allow her to dump Caylee on them at night. She was in a box as her parents started to come down on harder for not being able to prove she was working, for not taking care of Caylee, for confronting her about stealing, etc. But instead of being able to say "F U" and leaving with the baby to go hang out, like she did with Ricardo, who allowed Caylee in his bed, Tony would not allow it. Fed up and not able to continue her party girl lifestyle because of her "little snothead", she killed Caylee. This is a big deal when it comes to motive which must be shown even though it is not legally required to be shown.