Calculate variables within family in a long format dataset

I have a data set like this one:

df <- data.frame(FAMID = c(1,1,2,2,3,4,5,5,6),                 IID =   c("A","B","A","B","A","B","A","B","B"),                 Value = c(3,6,3,5,6,7,0,4,4))#   FAMID IID Value# 1     1   A     3# 2     1   B     6# 3     2   A     3# 4     2   B     5# 5     3   A     6# 6     4   B     7# 7     5   A     0# 8     5   B     4# 9     6   B     4

And I need to calculate some variables (the difference score for the variable Value and the mean, for each pair of members). So, I would need an output like this one

df2 <- data.frame(  FAMID2 = c(1,1,2,2,3,4,5,5,6),  IID2 = c("A","B","A","B","A","B","A","B","B"),  Value2 = c(3,6,3,5,6,7,0,4,4),  DiffValue = c(-3, 3,-2,2,NA, NA, -4, 4, NA),  Mean = c(4.5,4.5,4,4,NA,NA,2,2,NA))#   FAMID2 IID2 Value2 DiffValue Mean# 1      1    A      3        -3  4.5# 2      1    B      6         3  4.5# 3      2    A      3        -2  4.0# 4      2    B      5         2  4.0# 5      3    A      6        NA   NA# 6      4    B      7        NA   NA# 7      5    A      0        -4  2.0# 8      5    B      4         4  2.0# 9      6    B      4        NA   NA

Is there any way to do it in a long format?

Thank you so much in advance.