Randomly sampling groups, followed by sampling within these sampled groups

My dataset contains several groups and each group can have a different number of unique observations. I carry out some calculations by group (simplified in the code below), resulting in a summary value for each group. Next, for the purpose of a bootstrap, I want to:

1. Randomly sample the groups with replacement (number of sampled groups = equal to number of different groups in the original dataset)
2. Within these sampled groups, randomly sample observations with replacement (number of sampled observations per group = equal to number of unique observations in that group in the original dataset)

A simplified version of my data set up (data1):

data1:

id    group  y
1001  1      10
1002  1      15
1003  1      3
3002  2      24
3003  2      15
3005  2      37
3006  2      32
3007  2      11
4001  3      12
4002  3      15
5006  4      7
5007  4      9
5009  4      22
5010  4      19

For the above, I some have code working for these steps separately, but I cannot seem to combine them:

# Calculate group value
y.group <- tapply(data1$y,data1$group,mean)

# Step 1. Sample groups, with replacement:
sampled.group <- sample(1:length(unique(data1$group)),replace=T)

# Step 2. Sample within groups, with replacement
data2 <- data.frame(data1 %>%
   group_by(group) %>%   # for each group
   sample_frac(1, replace = TRUE) %>%
   ungroup)

Obviously, the code above in full does not do what I want, as in step 2 the sampled groups from step 1 are ignored since it just uses the original group var. I have tried to solve this using step 1 and trying to generate a new dataframe containing only the sampled groups' observations (with duplicates if a group was sampled more than once, which is likely to happen), and then apply step 2 to that new dataframe, but I cannot get this to work.

I think I am just on the wrong path or overthinking things. Hopefully you can give me some advice on how to proceed.