i.e. "It is important," his mother replied, "(a/A)nd we will all have a great time."
"Not unless the second part of the quote starts a new sentence," J.R. said. "In that case, you'd start with a capital letter.
"However, if both halves are part of the same sentence," J.R. continued, "then the second half begins with a lower-case letter."
If a direct quotation is interrupted mid-sentence, do not capitalize the second part of the quotation.
"I didn't see an actual alien being," Mr. Johnson said, "but I sure wish I had."