Please, please, please (!!!) note the difference between "last rights" ("rights" is a word that means "legal claims", as in, "she has the rights to her late husband's property") and "last rites" ("rites" is a word that means, "religious ceremonies", as in, "the priest gave the last rites to the man on death row").

The Latin phrase you show should be spelled, "et cum spiritu tuo" (four words). It is used in the Latin mass (but I don't think it's part of the "last rites", which are said over a dying person). It is the congregation's response to the officiant's words, "Deus vobiscum", which means, "May God be with you." The Latin word here shows there're more than one person listening; the "you" is plural.

There are two forms to the English response. The phrase "and with your spirit" is modern English. The phrase "and with thy spirit" is archaic, using the word "thy" which shows that there is one person listening; the word "thy" refers to the singular "thou", just as the Latin word "tuo" refers to a singular Latin "tu".

Note that "priests" may speak to "criminals" in an infinite number of possible contexts, not only to perform last rites before an execution. The information you supply about the context here is not particularly clear. Fortunately the phrase itself is generally restricted to use in the Latin mass.