By homeplanet, I assume you mean place of birth? They were born there(coruscant), however they spent they spent several of the early years of their lives on the secluded world of Anoth(Sp?). Following this, they resided on Coruscan for a number of years, before relocating to Yavin iv for the length of the YJK books. During the NJO, I don't think they really had a home, they were all over the place for the better part of a year, the closest thing to home being Ralroost I guess...
in Dark Journey Jaina mentions the place she's lived and called them more of residences, not "Home." Joey
They were born on Coruscant and spent the first month or so of their lives there until the Empire retook the planet and forced the New Republic to retreat from Coruscant at which time they ended up on New Alderaan under the protection of Winter. They remained here during the whole of the campaign against Palpatine which saw the loss of the NR Star Destroyers Liberator (lost while on a mission to Coruscant), and Emancipator (lost during the Battle of Calamari), the Battle of Calamari, the threat of the World Devastators, the loss of Palpatine's flagship Eclipse, and a death for Palpatine. In fact they remained here through most of the tenth year after the Battle of Yavin and would appear to have seen their first birthday here. It was only when Imperial forces invaded New Alderaan that they had to be moved. They'd then spend the last little bit of 10 ABY at the Nespis VIII space city/station until it was destroyed. Anakin was born on the Nespis VIII space city/station. From there, they spent early 11 ABY on Onderon. At some point after Palpatine's final defeat they ended up on Anoth and saw their second birthday there. Before the end of the year, probably about midway through the year, in fact, they returned to Coruscant. At fourteen they started attending the academy. However, the YJK book The Lost Ones would seem to suggest that the school year at the academy does not last full year, at least not for students the twins age, as they returned to Coruscant for a short period of time.
It will be interesting to discover which planet the original Star Wars Twins, Luke & Leia, are born on. Episode III will thankfully answer this question.