Hi Jemaco
Because your uncle was born under 100 years ago, you'll likely have to pay for certificates rather than access them online.
If I was you, I'd gather all the information you (or other members of your family) have about Robert. Where and when born, where and when died, was he married etc. Then order certificates you don't have from the National Registers.
In relation to his time in Rainhill, the archives at Liverpool Library might be able to help you to find out what patient records (if any) still exist for the time he was there. Again, access to records can be a problem if the person is still alive or the stay was relatively recent. But the fact that you are a close family member may make things easier. Best to find out when he was there and then speak to the archivist responsible for those records.
Good luck. Hope you find something helpful.
Sarah