That masters and padawans share a close bond is restated in the Ahsoka novel when she tries to find Anakin in the Force and can't, thus she assumes he died.
Years later she does encounters someone familiar, but tries her best to not believe it, cause what she's found goes against everything she knew about Anakin Skywalker. And in some respects she was correct. As far as Darth Vader is concerned, Anakin Skywalker is dead. But he's not....not completely. He is just buried under layers of anger, pain, self-hatred, and despair.
Vader doesn't recognizes his children in the Force because he never really felt them in the Force before. He was away for much of the war, and only found out Padme was pregnant late. He didn't know she was having twins. He might have brushed one of them in the Force, but honestly, by that point, Anakin was having nightmares and it was becoming difficult for him to focus from all appearances. At least when it came to simple things. He was getting twisted around by both Palpatine and the actions of the Jedi Council. He really wanted to run, but because of his visions of Padme's death, he just couldn't think.
Darth Vader did feel the Force from Luke over the Death Star and commented on it. That plus the destruction of the Death Star made him very curious about who took out the Death Star. He did encounter Luke later on and realized he was the boy that had been with Obi-wan on the Death Star...but Luke was fairly weak in terms of training and no worth the effort to Vader....but his lightsaber, though...that sparked some interest. Followed by Boba Fett tracking down this rebel pilot's name as Skywalker. That set Vader off. Palpatine had lied to him. Not only that, but now, for the first time since Padme died.....Vader had a potential future.....Anakin Skywalker had a potential future. That changed things.
Poking around Luke's head for a weakness to exploit over Endor was how he found out about Luke having a twin sister. I don't know if he figured out that was Leia on the spot, or if that was something he picked up after becoming a Force Ghost. It is possible that Leia is naturally very good at hiding her Force potential. Or just that because she almost never used it means no one important noticed.