I am almost out of your situation (they're old enough to walk the majority of the time thank goodness). How I carry depends on where we are.
At home, outside - open carry, usually small of back where the gun is not going to get caught on small legs and I can use both hips for carrying kids, feed, whatever and still bend over to weed/trim/mow/etc.
In our home - left in locked safe (yes I know, not the most popular option for most members of this forum).
Shopping/in public, winter - I have an ultra attractive Carhart knockoff that has a pocket on the inside that zips - gun goes in that in a pocket holster.
Shopping/in public, remainder of year - purse carry (yep, ultra-unpopular around here).
I'm a large woman, IWB only works for me if I'm carrying ONE kid and don't plan on bending over much. IWB hurts me when I ride in a car and it is not easy to conceal in anything other than jeans and a baggy sweater. I tried a smart carry (like the cornered cat lady), and just could not figure out how to make it work for anything other than OC. I haven't found an ankle carry holster that my pants leg will fit over (sorry, I don't wear bell bottoms, and even boot cut jeans are tight around an ankle holster. Shoulder holster is just not practical for carrying two kids (I have one, I've tried it). Pocket carry is a great idea, but my pockets aren't big enough to carry even a Ruger LCP in. Fanny packs are problematic, rarely complement the wardrobe, especially at more formal functions and are painful for the child riding ontop of the hip with the fanny pack on it (in my case the child had the sights and hammer poking him in the diaper area or in the leg. Bra carry is an uncharted frontier for holster makers, but for many women would be more feasible than IWB.
You'll find lots out there about carrying ONE kid, but two?? very little.
For the anti-purse carry, I respect their reservations, but I don't feel I'm being irresponsible simply because I purse carry. I can sling my purse and diaper bag across my torso and carry two children quite well for long periods of time. For every anti-purse carry reason, I can counter with my reasons as to why I feel safer purse carrying than not carrying. This is not an ideal world, I do the best I can.
Thanks for posting the question, I'm always on the lookout for new ideas!