I had a similar problem. I had replaced the failed alternator a few years ago with an higher output one. Last summer, I noticed the no charge at idle problem. I replaced the alternator again under the warrantee. That didn't fix the problem. I took my Yukon to the dealer for an unrelated issue and they noticed that the idle was low. They did a fuel system cleaning. The idle went up about 1 or 2 hundred RPMs. That solved the problem. My air conditioner now works better at idle too. That was about a year ago and I haven't seen the problem since. I don't remember the cost but I think it was around $125 but it was defiantly less that $200. My Yukon is a 2001 with over 300k miles and the original injectors. The results proved it needed a good cleaning and the over the counter cleaners were not doing the job.
Someone's earlier suggestion to upgrade the output cable is a good one. I replaced the wimpy factory cable with a 2 gauge cable as part of the "big 3" upgrade. It cost me 50 or 60 dollars for all three cables and battery lugs. It provides a much better path for power. I used 2 guage cables for all three cables. I think the voltmeter doesn't drop as much at higher power draws. I admit that this may be my imagination. There are plenty of articles online explaining what the big 3 upgrade is. The articles are usually generic. If you need me to explain exactly what I did, let me know.