I have two young children so it's always a balancing act. I'm a hands-on Dad so the killer for me was the weekend long runs - xc marathon and an xc half at the very least every weekend.
However, I've heard said that if you can cover the race distance in your combined weekly runs every week, however you split it up, then you've probably got enough in the bag to get round the course so long as you stay injury free. Some one will probably shoot me down in flames for saying it but that makes fitting your runs in round your family much easier.
And unless you're competing at the front, there's really no point in pushing yourself too hard and risking injury. I can run 10k with sore calves, or blisters, or a tight IT band, but 50 miles? No thanks.
There have been times* when I have not even managed to get round my bog standard 6 mile trot without the need for an investigation of the scenery.
I think you need to review your diet if you struggle to do a 6 mile jog without the need for a sh1t. Why don't you go to the toilet before your run? And I bet you don't clean up after. Quite disgusting and totally unnecessary.
You can't force one out just because you're going for a run. I'm not a "regular" person and can often go days (or a week if away on holiday) without a number 2. All the rocking and popping in the world isn't going to make me plop to order.