I reread those chapters from the book. It seems quite clear:

Mrs. Bennet assured her that they never sat there after dinner, and then added,

``May I take the liberty of asking your ladyship whether you left Mr. and Mrs. Collins well.''

``Yes, very well. I saw them the night before last.''

and then:

A report of a most alarming nature reached me two days ago. I was told that not only your sister was on the point of being most advantageously married, but that you, that Miss Elizabeth Bennet, would, in all likelihood, be soon afterwards united to my nephew, my own nephew, Mr. Darcy. Though I know it must be a scandalous falsehood, though I would not injure him so much as to suppose the truth of it possible, I instantly resolved on setting off for this place, that I might make my sentiments known to you.''

She also says:

Do you then pretend to be ignorant of it? Has it not been industriously circulated by yourselves? Do you not know that such a report is spread abroad?

which suggests that she learnt about it as about something certain rather than a speculation. After all she insists on knowing if they are engaged already.

Then in his letter to Mr. Bennet Mr. Collins writes:

``My motive for cautioning you is as follows. We have reason to imagine that his aunt, Lady Catherine de Bourgh, does not look on the match with a friendly eye.''

and

``After mentioning the likelihood of this marriage to her ladyship last night, she immediately, with her usual condescension, expressed what she felt on the occasion; when it become apparent, that on the score of some family objections on the part of my cousin, she would never give her consent to what she termed so disgraceful a match. I thought it my duty to give the speediest intelligence of this to my cousin, that she and her noble admirer may be aware of what they are about, and not run hastily into a marriage which has not been properly sanctioned.''

It seems clear then that the Collinses together dined at Rosings and shared the information. It is possible Charlotte didn't want to share, but we know Mr. Collins would anyway. The next morning Lady Catherine left for Hertfordshire. She had to sleep somewhere on her way (maybe London) because she came to Longbourn in the morning. It seems there was no delay in her coming. I don't think she'd visit Darcy first because she probably thought he was in Netherfield. Probably she went there even before talking to Lizzy and seeing he wasn't there she went to meet Lizzy and then Darcy in London.

However, I think that to Mr. Collins' attitude we might also add his own rejection. He might care about Lady Catherine's opinion, but surely he wouldn't be happy if that upstart missy who dared to reject his own offer married so well after all.