I agree that Lorelai always thought she knew best when it came to kids. She did it with Jess when she tried to tell him she understood how he felt when in fact, she had no idea what Jess had to go through. She stuck her nose in when Luke specifically asked her not to and said he could handle it. But she thought she knew best and from that moment, she hated Jess just because he acted like that on his first day of being in Stars Hollow. I agree that she was quite patronising and condescending towards Luke with Jess and April, implying that he didn’t know anything at all about looking after a kid. She was trying to butt her way in instead of just being there and encouraging him. I’m not saying Luke didn’t handle the April situation well but Lorelai was too full on as well and in times, I feel like she was a bit rude and she was making fun of him, eg, April’s birthday present. I don’t blame Luke for getting defensive.
Lorelai also did it with Lane to an extent, trying on numerous occasions to reason with Mrs Kim. I know she meant well but she and Mrs Kim were very different. She should have respected that.