Aww bless you Southernchic
I have 2 cats that I adopted from the rescue centre and they have been the best! I had a home check for the second cat I adopted, the first one I just went to the centre chatted with them a while and picked her up a few days later. They said they would visit the home at a later date but 3 years later I wait
As for the home checks I think they will vary from centre to centre so it would be hard to give a play by play definitive account.
The checks are really more about seeing if the cats will be fine with you and that you are a good person to look after them. I had a home check for my second cat, in fact, I had it before I was allowed to chose a cat. I was asked about work etc and how my other cat was in relation to her temperament -fortunately she was on her best behaviour but she is a placid pud anyway. We sat in the living room, had a cuppa and chatted for a bit. They certainly didn't go looking around my home or checking anything like that. But that was my experience. Personally, I think the home visit is used so that they get a general feel for you as a person and how you would look after kitty and her mum!
I am excited for you.
I want another cat now! But 3 may be too much for my house.
The tip is to just relax, be yourself and you will be fine. At the end of the day you are offering a much needed, loving home to the puds and I am sure it will be very much appreciated, snd you will have two very happy cats!!