wow, that was some answer! worked for ages.. now it doesn't
To be fair, this is the very first time you've mentioned that it USED TO WORK, BUT NO LONGER DOES.
, with any card, any size.. can read but not write... just use an external card reader. ok.
Well, sometimes the "solution" just involves finding a hardware workaround that works, if there's no other software-related solution available. Once you've invested heart and soul and many hours, days or weeks trying to figure it out and fix it, and still not succeeded, maybe just accepting an alternative approach that provides exactly what you've been wanting to achieve is just the best you're going to get. Like trying to find parts for or a total replacement for something that "they don't make anymore". At some point, you have to admit "they don't make it anymore".
... thought some people like to get to the bottom of things, try to figure out what changed to make it just stop working.. guess not here
Actually, we're really mostly all about trying to help and get your problem resolved. We have no idea what, if anything, changed in your environment with your own PC if you don't tell us what changed. So far, from what you've provided us it appears nothing has changed, so there shouldn't be anything different about why you used to be able to write to these cards and you no longer can. And yet... you have this symptom.
Most likely explanation is a hardware defect, that simply occurred. Like a hard drive failing, or a piece of electronics just going out. Why did that happen when it never happened before? Who knows? Just did. Solution? Replace it.
Hardware failures that just suddenly appear are much more likely explanations for your symptom than "driver software which seemingly goes out of commission, and will be resolved by uninstall/reinstall".
You can try and get HP to replace the card reader in your PC, which is the most likely true solution that will be guaranteed to work (since they will assume responsibility for guaranteeing it to you). Or, you can use your own external card reader, which also works.
The "getting to the bottom of it", in light of your statement that nothing's changed and that trying a reinstall of the internal SD card reader drivers didn't change anything, seems to point to a hardware solution... like replacing the card reader in your PC. Same as a panel going out in a laptop, which happens occasionally same as other occasional hardware failures occur over time. That's what manufacturer's warranty is for, or after warranty expires simply paying for replacement repair parts and service.
In your case, you've already got a working external card reader that can be used successfully to write to the card. Sounds like an acceptable solution, even though you'd like the now-failing reader in your PC to work as it once did. If it's that important to you, get HP to repair it, which wiill almost certainly involve replacing the card reader in your PC with a new one that is fully functional. HP will ensure it works.