Okay, I'll give my shot at it. Also note that for most purposes, I will only cosider Another and Home world dimensions, not Reptite dimension or RD dimension.
We originally have one dimension. The original dimension. Another World. As time progresses, we have Crono's quest, traveling through time, eventually defeating Lavos, and saving the planet's future. Time progresses, Chronopolis, the Time Crash, and other events that set up Chrono Cross. Now, we get up to 1010, Another World, timeline where El Nido now exists. In 1010, Serge is killed. But, something happend (we don't know), and he was saved from death, and this split off a new dimension from Another, [the one that split off was] Home.
Now, consider where on this chain of events that Crono and Co defeated Lavos. Per this chain of events, Crono and co defeats Lavos before Home is created. Because of this, Crono and co cannot time travel to a timeline that does not exist yet. Plus, they time travel from a period that is before the time split. Since there is only one set of Crono, at the time they time traveled to defeat Lavos, and now there are two dimensions, the only one he could have possible time traveled to was Another, since you cannot go from a time where Dimension X does not exist to the future in Dimension X.
That make any more sense?