This same issue has been on my mind a lot lately, since I have a 1-year-old son. You didn't say how old your children are - so I'll tell you my experiences so far over the last year.
FYI - I generally carry a Smith & Wesson M&P 45 full size, strong side (right side for me) in a kydex holster on my belt. I usually wear a vest or similar open-front cover garment.
In the first few months after my son was born, we carried him everywhere in the car seat, the kind with the carry handle. I quickly realized that I had to carry the car seat in my left hand - otherwise my gun would be pointed right at him. I also realized that a better option was to use the stroller to which the car seat attached.
As he got past 6 months, we changed to a front-facing car seat that remained in the vehicles. Using the stroller continued to be the best option while armed. On the occasions when I would carry him in my arms (either at my chest or on my right side), he would sometimes kick my gun. Not a big deal since the gun is drop-safe and the holster has excellent retention, but it would still nearly stop my heart.
I quickly realized that when I carried him in my arms, it was best to shift him to my left side. In addition to keeping his little feet away from my gun, carrying him on the left side would allow me to put my body between him and the attacker, while also allowing me to access and draw my gun. I am attaching two photos to illustrate this. Yes, my little boy is in both photos.
Link RemovedLink Removed
Please note - the gun in the photos was verified unloaded by myself and my wife, chamber was flagged, and it was always pointed in a safe direction.
I would not recommend off-body carry such as a purse or fanny-pack, mainly because you need two hands to draw, and you want to have at least one hand free to manage your child / children, or to fend off an attacker while drawing.
I would definitely not recommend a shoulder holster. If you carry your child on your weak side your holster is obstructed. If you carry your child on your strong side, your shooting hand is occupied.
So, you need to think in terms of:
- Is my firearm drop-safe and impact-safe?
- Does my holster adequately guard the trigger against an accidental activation?
- Does my holster offer adequate retention against an unexpected grab or kick from a child?
- Does my method of carry allow for access and presentation while I am carrying or otherwise minding my child/children?
- What method of carrying or transporting my child will be most conducive to carrying a handgun as well?
In short - try to think about the whole picture, rather than just the method of carry.
Hope this helps!
