If your dog rolls in cow poo, cover the offending area, ie the dog, in tomato ketchup and let it dry, then rub it off. Apparently this gets rid of the smell immediately, your dog just smells a little tomatoey!
We got a pup (boxerX) a few weeks ago. Ds twins are just over 2. It is very very hard going, if you are getting a pup it is a good idea to buy a dog crate. Not to lock the dog up all the time. But we found that when he went into the cage he would bark when he needed the toilet. So he is now fully house-trained at 11 weeks old. Okay there are still accidents but it isn't as bad as some people have it. Paper training is horrendous with toddlers in the house. Believe me.
You may think a crate is cruel but you are not imprisoning the dog and he (or she) will find it a place to rest, away from the children. My two know that if Tag goes into his crate then they must leave him alone to sleep. I can leave him alone in the house for short periods, never more than a couple of hours and not every day, and know that while he is in his crate he is happy and the house is not going to be wrecked! I know some people put their dogs in crates all day but I think the longest they are advised to be left is 5 hours.
Biting is a problem, they just won't tell him no, but as I don't leave them alone with him I do the ordering about. I sprayed their socks with Bitter Bite to put him off and it worked!
But it is really hard going sometimes and I am glad when DH comes home to take him out a walk! Still, there are meant to be lots of benefits to children growing up with dogs - the way they treat animals etc. Just do it only if you want to, remember they won't be the ones looking after it, you will.