Rather than "putting them on the back-burner" (which disrespectful act Jesus would never do to his mother since it would be breaking one of the 10 commandments), Jesus was simply using the occasion of their arrival to emphasize that those who hear the Word of God and keep it are as close to him as his family. This includes his mother, by the way, who we are told is blessed among women "because she believed that there would be a fulfilment of what was spoken to her from the Lord." (Luke 1:45)
Do you ever cook on a multiple burner stove? ‘Putting them on the back burner’ is not tossing burnt food in the trash, or even a diss, but an ‘I’ll get to that when it’s time to’.
When made aware of their presence, he didn’t immediately drop his teaching and go see to their needs, putting everyone else ‘on the back burner’. Yes, he did use the moment to make a point about God’s family
He was careful, addressing her as ‘woman’, not including her as one of the twelve, etc. The Lord was also careful not to elevate her in the eyes of others, not wanting her to become a focal point of idol worship, as the forerunner of the RCs tried to do:
“..a certain woman of the company lifted up her voice, and said unto him, Blessed is the womb that bare thee, and the paps which thou hast sucked. BUT, he said, Yea RATHER, blessed are they that hear the word of God, and keep it.” Luke 11:27,28
Note: the Word says ‘But’(changing directions), and says ‘yea rather’ (no comma between those two words), in a swift motion agreeing and directing attention to his chosen requirements of Godliness.