Assuming things are in order and you don't have to do any actual pattern matching, the answer could be as simple as:

# bind them together to form one dataframe
result.df <- cbind(df1,df2)
# rearrange the columns using a pattern of numbers
result.df <- result.df[,as.vector(t(cbind(1:50,seq(51,150,2),seq(52,150,2))))]

Since there would be a regular pattern of numbers by which to arrange the columns of the two dataframes you can specify the patterns and then get them in a series of numbers to interleave the columns as you wish. (also assumes your first df is 50 columns and the second has twice as many - the code be easily modified to use the actual number).

edit: if you have to perform pattern matching because the columns of the data frames are not in any coordinated order, you can use a similar strategy, but it's a little more complicated. See below - first a toy example with vectors matching your names, then the code applied to data frames.

### Proof of principle using simple vectors
# create allele names
df1 <- paste("Geno", 1:10, sep="")

# create genotype names
df2 <- paste("Geno", rep(1:10, each=2), c(".GT",".AD"), sep="")

# find the matching genotype and depth for each allele
gt.iv <- match(df1,sub(".GT","",df2))
ad.iv <- match(df1,sub(".AD","",df2))

# randomly scramble df2
df2 <- df2[sample(1:length(df2),length(df2))]

# combine all data
alldata <- c(df1,df2)

# order the combined data
alldata[as.vector(t(cbind(1:length(df1), gt.iv+length(df1),ad.iv+length(df1))))]

### apply the strategy to columns of dataframes called df1 & df2
# create two data frames
# alleles w/fake data
df1 <- data.frame(matrix(sample(c("0/0","1/0","0/1","1/1"),20,replace=T), nrow=2, ncol=10))
colnames(df1) <- paste("Geno", 1:ncol(df1), sep="")
# genotypes w/fake data
df2 <- data.frame(matrix(sample(1:100,20), nrow=2, ncol=20))
colnames(df2) <- paste("Geno", rep(1:(ncol(df2)/2), each=2), c(".GT",".AD"), sep="")

# add chaos to df2
df2 <- df2[,sample(1:ncol(df2),ncol(df2))]

# find the matching genotype and depth for each allele
gt.iv <- match(colnames(df1),sub(".GT","",colnames(df2)))
ad.iv <- match(colnames(df1),sub(".AD","",colnames(df2)))

# combine all data
alldata <- cbind(df1,df2)

# order the combined data
alldata <- alldata[,as.vector(t(cbind(1:ncol(df1), gt.iv+ncol(df1),ad.iv+ncol(df1))))]

One-off solution:

tmpResult = cbind(df1,df2)
result = tmpResult[,order(colnames(tmpResult))]

This assumes the colnames are as given in the post.