13 V.S.A. § 3705(e) states as follows:
(e) A law enforcement officer shall not be prosecuted under subsection (a) of this section if he or she is authorized to serve civil or criminal process, including citations, summons, subpoenas, warrants, and other court orders, and the scope of his or her entrance onto the land or place of another is no more than necessary to effectuate the service of process.
The statute is thus quite broad allowing the police office to enter upon your property to effect service of any civil or criminal process, specifically including citations. So the answer to your question of whether the cop may enter upon your land to serve you another citation is clearly yes.
Even if it was trespass (and it’s not, but I’m discussing it just to play this out), that would not make the service invalid, it would just make the officer subject to criminal prosecution for trespass. And do you really think the local police department for whom he works and the local prosecutor who works along side them would really prosecute the officer for trespass for this? I think that would be pretty unlikely.