The first thing you have to understand is that even though vampires can make more vampires they don't build coffins! A vampire can create a vampire spawn by killing it with it's drain ability this dose not fabricate a coffin.
"If reduced to 0 hit points in combat, it automatically assumes gaseous form and attempts to escape. It must reach its coffin home within 2 hours or be utterly destroyed. (It can travel up to nine miles in 2 hours.) Once at rest in its coffin, it is helpless. It regains 1 hit point after 1 hour, then is no longer helpless and resumes healing at the rate of 2 hit points per round." This is the only rule on vampires around this stipulation cause their not meant for players to play they are story plot and villains.
As for your question yes you can have a mobile coffin the rules for this are found in other sources outside the regular DnD 3.5 but they convert effortlessly:
The coffin must rest a single day with the vampire inside and out of sunlight for it to qualify as his/her coffin and then from that point on its the coffin that he/she must return to.
A vampire who has no coffin can return to their grave(if they were buried) but not the room/place of death and rebirth that occurred to change them into a vampire.
A vampire who has a coffin who wishes to travel must move his coffin to a new location and rest in it for a complete day and there must be no sunlight that can reach the coffin.
Yes destroying the coffin of a vampire forces him to make a new one or suffer true death after his 2 hours of looking fail.
The sources for this come from too many books to list but they don't apply any stats or change based on other factors so they can fit any DnD 3.5 game.