Just wanted to document my steps related to this problem. 
Say I execute this in a terminal: 
~$ echo "read -p 'Press Enter'" > mytest.sh
~$ chmod +x mytest.sh
~$ bash -c bash
~$ bash -c ./mytest.sh
... and leave it waiting at the read input prompt. Then, I can always find the pid of mytest.sh like: 
$ ps axf | grep mytest
20473 pts/2    S+     0:00              |   |   \_ grep --color=tty mytest
20308 pts/5    S+     0:00              |   |       \_ bash -c ./mytest.sh
... however, I'd like to output a ps axf tree limited to some parent of mytest.sh; looking at a full ps axf, we can see a hierarchy: 
$ ps axf
 1489 ?        Sl     1:39              \_ gnome-terminal --sm-client-id 106ab86
 1511 ?        S      0:00              |   \_ gnome-pty-helper
...
20238 pts/5    Ss     0:00              |   \_ bash
20274 pts/5    S      0:00              |   |   \_ bash
20308 pts/5    S+     0:00              |   |       \_ bash -c ./mytest.sh
...
Then, say I don't want to 'scan' the gnome-terminal (1489) as parent, but instead I want to start at bash (20238).. So, I'd like to obtain this output: 
$ ps f -p 20238 20274 20308
  PID TTY      STAT   TIME COMMAND
20238 pts/5    Ss     0:00 bash
20274 pts/5    S      0:00  \_ bash
20308 pts/5    S+     0:00      \_ bash -c ./mytest.sh
... except, I don't want to copy/paste the child PIDs manually :) 
I could use pstree: 
$ pstree -a -p 20238
bash,20238
  └─bash,20274
      └─bash,20308 -c ./mytest.sh
$ pstree -p 20238
bash(20238)───bash(20274)───bash(20308)
... unfortunately, the output is not exactly the same as in ps axf, which I prefer.
So, I can use pstree simply to obtain child PIDs: 
$ pstree -p 20238 | sed 's/(/\n(/g' | grep '(' | sed 's/(\(.*\)).*/\1/'
20238
20274
20308
$ pstree -p 20238 | sed 's/(/\n(/g' | grep '(' | sed 's/(\(.*\)).*/\1/' | tr "\n" ,
20238,20274,20308,
and then use those to obtain a ps axf tree, based only on the PID of the parent: 
$ ps f -p $(pstree -p 20238 | sed 's/(/\n(/g' | grep '(' | sed 's/(\(.*\)).*/\1/' | tr "\n" " ")
  PID TTY      STAT   TIME COMMAND
20238 pts/5    Ss     0:00 bash
20274 pts/5    S      0:00  \_ bash
20308 pts/5    S+     0:00      \_ bash -c ./mytest.sh
Well, hope this helps someone,
Cheers!