Force mounting an external disk that is not recognized
Just when I was about to give up, format the drive and lose my data, somehow I was able to fix the drive so I am posting what exactly I did in terminal for the benefit of other people who might come across this post and have the same problem. I hope this will be helpful to somebody:

Admins-MacBook-Pro:~ admin$ diskutil mount /dev/disk3
Volume on disk3 failed to mount; if it has a partitioning scheme, use "diskutil mountDisk"
If the volume is damaged, try the "readOnly" option
If the volume is an APFS Volume, try the "diskutil apfs unlockVolume" verb
Admins-MacBook-Pro:~ admin$ mount force /dev/disk3
mount: You must specify a filesystem type with -t.
Admins-MacBook-Pro:~ admin$ mount -t /dev/disk3
Admins-MacBook-Pro:~ admin$ mount force -t /dev/disk3
usage: mount [-dfruvw] [-o options] [-t external_type] special node
       mount [-adfruvw] [-t external_type]
       mount [-dfruvw] special | node
Admins-MacBook-Pro:~ admin$ mount -t force /dev/disk3
usage: mount [-dfruvw] [-o options] [-t external_type] special node
       mount [-adfruvw] [-t external_type]
       mount [-dfruvw] special | node
Admins-MacBook-Pro:~ admin$ diskutil verifyDisk /dev/disk3
Nonexistent, unknown, or damaged partition map scheme
If you are sure this disk contains a (damaged) APM, MBR, or GPT partition
scheme, you might be able to repair it with "diskutil repairDisk /dev/disk3"
Admins-MacBook-Pro:~ admin$ diskutil repairDisk /dev/disk3
Nonexistent, unknown, or damaged partition map scheme
If you are sure this disk contains a (damaged) APM, MBR, or GPT partition map,
you can hereby try to repair it enough to be recognized as a map; another
"diskutil repairDisk /dev/disk3" might then be necessary for further repairs
Proceed? (y/N) y
Partition map repair complete; you might now want to repeat the
verifyDisk or repairDisk verbs to perform further checks and repairs
Admins-MacBook-Pro:~ admin$ diskutil repairDisk /dev/disk3
Repairing the partition map might erase disk3s1, proceed? (y/N) y
Started partition map repair on disk3
Checking prerequisites
Checking the partition list
Adjusting partition map to fit whole disk as required
Checking for an EFI system partition
Checking the EFI system partition's size
Checking the EFI system partition's file system
Checking the EFI system partition's folder content
Checking all HFS data partition loader spaces
Checking booter partitions
Reviewing boot support loaders
Checking Core Storage Physical Volume partitions
Updating Windows boot.ini files as required
The partition map appears to be OK
Finished partition map repair on disk3
Admins-MacBook-Pro:~ admin$


Since I've tried pretty much every terminal line under the sun, I think the key was the sequence in which this worked, which was:

mount -t /dev/disk3
mount force -t /dev/disk3
diskutil verifyDisk /dev/disk3
diskutil repairDisk /dev/disk3
diskutil repairDisk /dev/disk3


When I heard tried to verifyDisk and repairDisk a few days ago it had not worked but somehow with this sequence it was able to repair the partition map

Thank you to all of you guys who have tried to help me with this.
I am glad to have my data back ;)