Positive @ Home but Negative @ Hospital / Clinic Urine Pregnancy Test?

Is it possible?
Yes, very!

Most of the UPT (Urine Pregnancy Test) in Government Hospital / Clinic can be less sensitive.
Not sure what's their sensitivity level is BUT, through personal experience, at a beta HCG (blood) of 70 miu/ml, the Government Hospital's UPT came back "negative", several times.

Even when my beta HCG was at 180+ miu/ml , UPT was first reported as negative, then 'faint positive'.

HCG in theory will double every two days, so, if you are getting a faint positive on your UPT at home, give it a couple of days and test again.

Also, sometimes "chemical pregnancy" happens.
Or in a simpler term, 'lil bean did not manage to stick on.

So, if you are planning to test early (days before your period is due), you must remember the possibility of  "chemical pregnancy". It can be emotionally devastating.