You can do that with su or sudo, no need for both.

sudo -H -u otheruser bash -c 'echo "I am $USER, with uid $UID"' 

The relevant parts of man sudo:

-H   The -H (HOME) option requests that the security policy set

     the HOME environment variable to the home directory of the

     target user (root by default) as specified by the password

     database.  Depending on the policy, this may be the default

     behavior.

(Starting from Ubuntu 19.10, -H is no longer needed as this is now the default behaviour. See: How does sudo handle $HOME differently since 19.10?)

-u user     The -u (user) option causes sudo to run the specified

      command as a user other than root.  To specify a uid

      instead of a user name, use #uid.  When running commands as

      a uid, many shells require that the '#' be escaped with a

      backslash ('').  Security policies may restrict uids to

      those listed in the password database.  The sudoers policy

      allows uids that are not in the password database as long

      as the targetpw option is not set.  Other security policies

      may not support this.

su can only switch user without providing a password if you are root. See Caleb's answer

You can modify the /etc/pam.d/su file to allow su without password. See this answer.

If you modified your auth file to the following, any user that was part of group somegroup could su to otheruser without a password.

auth       sufficient pam_rootok.so

auth       [success=ignore default=1] pam_succeed_if.so user = otheruser

auth       sufficient   pam_succeed_if.so use_uid user ingroup somegroup

Then test from terminal

rubo77@local$ su otheruser -c 'echo "hello from $USER"'

hello from otheruser