Sourcing bash file is not exporting its definitions when running with bash -c

Question

I'm having a hard time trying to describe this issue, but here is my best shot.

I want to:

• write a bash script that contains variable definitions. I will refer to this as file as DEF_FPATH .
• write another bash file that uses those definitions. I will refer to this file as USAGE_FPATH .
• execute that second file in an isolated subshell.

My issue is that when I directly execute source "$USAGE_FPATH" in my current bash session it works fine. But that's not quite what I want. I want to invoke a new bash instance and call it like this: bash -c "source '$USAGE_FPATH'" , but this does not seem to work.

I have a MWE that demonstrates the problem:

#!/bin/bash
__doc__="
This is a MWE illustrating an issue where using 'bash -c' to source a file that
sources another file does not seem to work how I would expect it. 

Requires:
    sudo apt install cowsay
"
TEMP_DPATH=$(mktemp -d)


# Write a bash file containing some definitions
DEF_FPATH=$TEMP_DPATH/definitions.sh
echo '
#!/bin/bash
echo "[definitions] start"
alias mydef=cowsay
echo "[definitions] finish"
' > "$DEF_FPATH"


# Write a bash file containing some definitions
USAGE_FPATH=$TEMP_DPATH/usage.sh
echo '
#!/bin/bash
echo "[usage] about to source definitions"
source "'"$TEMP_DPATH"/definitions.sh'"
echo "[usage] about to use the definition"
mydef "hello world"
echo "[usage] finished"
' > "$USAGE_FPATH"


echo "Check DEF_FPATH looks ok"
echo "==============="
echo "DEF_FPATH = $DEF_FPATH"
echo "==============="
cat "$DEF_FPATH"
echo "==============="
echo ""
echo ""


echo "Check USAGE_FPATH looks ok"
echo "==============="
echo "USAGE_FPATH = $USAGE_FPATH"
echo "==============="
cat "$USAGE_FPATH"
echo "==============="
echo ""
echo ""


echo ""
echo ""
echo "Variant #1: Execute with source (this works)"
echo "-------------------"
source "$USAGE_FPATH"
echo "-------------------"


echo ""
echo ""
echo "Variant #2: Execute with bash -c (this fails)"
echo "--------------------"
bash -c "source '$USAGE_FPATH'"
echo "--------------------"

The MWE starts by writing the two files DEF_FPATH and USAGE_FPATH to disk. It then displays their contents as a sanity check to check I'm not misquoting something. The output of this section is:

Check DEF_FPATH looks ok
===============
DEF_FPATH = /tmp/tmp.p1NMaxTdM6/definitions.sh
===============

#!/bin/bash
echo "[definitions] start"
alias mydef=cowsay
echo "[definitions] finish"

===============


Check USAGE_FPATH looks ok
===============
USAGE_FPATH = /tmp/tmp.p1NMaxTdM6/usage.sh
===============

#!/bin/bash
echo "[usage] about to source definitions"
source "/tmp/tmp.p1NMaxTdM6/definitions.sh"
echo "[usage] about to use the definition"
mydef "hello world"
echo "[usage] finished"

===============

This seems fine. The initial definition script sets up the alias (which I imagine is hard to get wrong), and the second usage script is pointing to the correct path, so it should source the definition before it tries to use it.

The next part of the MWE demonstrates that this indeed works when invoking USAGE_FPATH via a source in the current shell. The output is:

Variant #1: Execute with source (this works)
-------------------
[usage] about to source definitions
[definitions] start
[definitions] finish
[usage] about to use the definition
 _____________
< hello world >
 -------------
        \   ^__^
         \  (oo)\_______
            (__)\       )\/\
                ||----w |
                ||     ||
[usage] finished
-------------------

However, the second variant where I try to use bash -c seems to encounter a problem.

Variant #2: Execute with bash -c (this fails)
--------------------
[usage] about to source definitions
[definitions] start
[definitions] finish
[usage] about to use the definition
/tmp/tmp.p1NMaxTdM6/usage.sh: line 6: mydef: command not found
[usage] finished
--------------------

It starts off by calling the usage script correctly. It displays output that indicates it is correctly sourcing the DEF_FPATH , but then it fails to find the mydef alias when it goes to use it.

My question is: why? What is the difference between invoking the outer script with source in the current shell versus invoking it in a new bash process with -c . I'm still using source in both instances, so I'm confused as to why the second variant fails. Is there another flag I'm supposed to be passing to bash to allow nested sourcing? Something else?