I don't kow much about it either but I did read a little about this online. I didn't find much info but what I did find said that when the AC only works when it is cool at night it could mean there is a small refrigerant leak in the system somewhere. Maybe your home warranty company can have a tech check your system for leaks. I read that the average size central AC holds 4 to 6 pounds of refrigerant so if the first tech put in 3 pounds, I would think that might indicate a leak in the system. Hopefully the warranty administrator can get a tech to check the system more thoroughly and get it fixed.
If the AC is outside, maybe one of its capacitors is bad or is getting hot during the day and not allowing the fan or the compressor to kick on. I went through some problems with the AC in my own house in the last two years. Two years ago my outside AC unit stopped working and it was because the capacitor that controls the compressor was bad. They call it a run cap. I bought a new run cap for it, about $50.00 at a very good local appliance parts/service/sales store here where I live. They checked the original run cap to be sure it was bad and I replaced the run cap, all was well until last year. Then the AC quit again, it turned out the other cap, known as a fan cap went bad. This is the cap that controls the compressor fan on the outside AC unit. I bought a new fan cap for about $35.00, replaced it and it was OK until this year. Last weekend the AC quit again. The fan motor had gone bad, the fan wasn't turning and the fan motor was so hot I could not touch it. I replaced the fan motor and bought a single cap that operates both the fan and compressor. This new cap is also better matched voltage-wise to the new fan motor.
I know none of that matters much with the problem you are having but maybe you could check your capacitor(s) or have them checked to see if they are getting hot and not allowing the system to turn on. I read online that the compressor should have a limit switch or safety switch that will turn it off if the refrigerant falls below a certain safe level.
I am no expert at all on this but it sounds like a leak or a heat-related power problem to me. I don't see how you could have bad caps or freon leaks on a two year old AC system but I guess anything is possible. I would say get the warranty folks to check the system again.