I think we need to review what "rest" means and what it does not mean lest we make the same erros as the Pharisees and lead people into bondage that God did not command. Forbidding going out for a walk on Sunday sounds absolutely horrendous to me.
"Now there is in Jerusalem by the Sheep Gate a pool, in Aramaic called Bethesda, which has five roofed colonnades. 3 In these lay a multitude of invalids—blind, lame, and paralyzed. 5 One man was there who had been an invalid for thirty-eight years. 6 When Jesus saw him lying there and knew that he had already been there a long time, he said to him, “Do you want to be healed?” 7 The sick man answered him, “Sir, I have no one to put me into the pool when the water is stirred up, and while I am going another steps down before me.” 8 Jesus said to him, “Get up, take up your bed, and walk.” 9 And at once the man was healed, and he took up his bed and walked. Now that day was the Sabbath. 10 So the Jews said to the man who had been healed, “It is the Sabbath, and it is not lawful for you to take up your bed.” 11 But he answered them, “The man who healed me, that man said to me, ‘Take up your bed, and walk.’ ” - John 5:2-11
"One Sabbath he was going through the grainfields, and as they made their way, his disciples began to pluck heads of grain. 24 And the Pharisees were saying to him, “Look, why are they doing what is not lawful on the Sabbath?” 25 And he said to them, “Have you never read what David did, when he was in need and was hungry, he and those who were with him: 26 how he entered the house of God, in the time of Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?” 27 And he said to them, “The Sabbath was made for man, not man for the Sabbath. 28 So the Son of Man is lord even of the Sabbath.” - Mark 2:23-28
"Remember the Sabbath day, to keep it holy. 9 Six days you shall labor, and do all your work, 10 but the seventh day is a Sabbath to the Lord your God. On it you shall not do any work, you, or your son, or your daughter, your male servant, or your female servant, or your livestock, or the sojourner who is within your gates. 11 For in six days the Lord made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy." - Exodus 20:8-11