No
She cannot be sent to trial as in all court cases it is Her Majesty the Queen Versus the defendant.
The law is the Queens law.
The Queen can issue a royal pardon so it would make sence if she could be arrested she would just pardon herself.
If a monarch has been arrested/imprisoned, they have probably been overthrown first.
The Queen is the embodiment of the law, and prosecutions are made in her name. She herself is above the law. The most obvious example is that any car owned by her is unregistered and has no number plates.
A while ago I asked this same sort of question, wondering what'd happen if she went beserk on a walkabout and kicked the crap out of someone. The general consensus was probably nothig much would happen to her, and the victim would become a celebrity.
"Strangling Prince Philip"... you're not the Queen are you, plotting something?