I think you definitely have tape 2 of the Godfather Trilogy. I have the complete 4-tape vhs box set. Tape 1 has virtually all the Robert De Niro scenes, as it is compiled in chronological order. I have just checked my tape 2, and it indeed starts with Vito recovering at home in bed, with Tom etc around. It ends with the fall of Cuba, Michael kissing Fredo ('I know it was you..') and Michael trying to get Fredo to get on the plane with him. Tape 3 has the rest of GFII plus GFIII, and tape 4 is the interviews and stuff (Godfather family - a look inside). One sure way to know if you have tape 2 of the trilogy is to see if your tape has the extra scenes in it - for example the scene where Michael is recovering in bed after the car bomb, the scene with Gardner Shaw in it at the Las Vegas party, and the scene where Fabrizzio gets blown up by the car bomb after closing up Fred's Pizza for the night, in revenge for killing Appollonia.
Anyway, I think you've been done mate - that tape makes no sense in isolation, you've got half of GFI and half of GFII. Time to put a horse's head in someone's bed!