Is saying "We will arrange to visit, God willing," with the intention of not visiting, considered a form of Tawriya (strategic ambiguity) or lying, and would the situation be rectified by amending the phrase to "If God wills and only God willing"?

The first statement contains no error or sin, because it ties the visit to Allah's will, which is correct. As for the statement "my circumstances do not allow it," there is no harm in it if one intends psychological, personal, or family circumstances. The second statement was clearer, but its content is the same as the first, and we hope there is no sin or breach of promise in that.