several hours without peeing

My kids are basically potty trained, have been in underwear since Thanksgiving, but sleep in diapers. One ushually wakes up dry, one almost always wet.
They sometimes still have accidents. I always ask them if they have to pee before we leave the house, and even if it's been several hours since they last went, they say no! My daughter who wakes up dry says she doesn't have to go in the morning, but when I make her sit on the potty just to try, she goes pees a lot! I know she must be holding it in..
I have to bribe them just to try to pee before leaving the house, sometimes they go, sometimes they don't, but I get nervous because this happens when we'll be out for a while and they may not have easy access to a potty, or they are going to someones house and I know they would be too shy to ask..
Does anyone have this?
Sometimes they will even try, not go, but I say if you go I'll give you xyz, then they'll go!
Sometimes when we are home, I'll ask if they have too, they'll say no, and I'll just ignore it, but I can't imagine them not having to go as it's been several hours, and they have been drinking a lot.. it doesn't make sense to me.
Anyone have this? Also at what age did you kids really just start to go by themselves, without needing assistane, going to pee and washing hands?
And at what age were they able to poop/wipe ect?

 

One of my DDs has almost never had an accident (except in her first few days of underwear). If she tells me she doesn't have to go, even if it's been hours, I believe her. (They're 6.5 now, but this has been the case since at least age 4.)

The other one also almost never had accidents, but she has a tendency to say she doesn't have to go and then suddenly she HAS TO GO NOW! She can hold it, but she whines and complains and says she's going to pee her pants (she never does), but it's stressful.

DH instituted a rule around age 4 that they both had to try to go potty before leaving the house. We don't even ask if they have to go -- they just have to sit on the toilet for at least 10 seconds. If nothing comes out in that time, fine. Like all rules, it took a while before they started doing it without complaining, but now it's pretty much second nature.

As far as when they started taking full responsibility for it, I'd say around age 4 also. But they were in daycare and I think it was easier because the bathroom was right in the room and everyone was coming & going all the time -- it wasn't like taking a lot of time away from their play to go pee. They still aren't very good at wiping, but they do (nearly always) wash their hands.

With poop, sometimes they still need help wiping at 6.5. It depends how soft the poop is.

 

We also have the rule that they should try to go before we leave the house. More often then not, they will go.
My DS has had a fear of public bathrooms and he has gone several hours without going because he would only use the potty in a home environment. For the first time, he used the potty at the playground last night and I feel like he has turned a corner. Both of them are just starting to really go to the bathroom without assistance. The only issue is that our toilet and sink are high and they both have to use a step stool to reach both.
As for pooping, they do wipe themselves but I always ask them to let me know when they are done, so I can go over it. Sometimes I was not needed and sometimes they do need an extra wipe from me.

 

You could try leaving a portable potty in your car or something, just in case... Otherwise, I can't really tell as we're just barely getting there. They do however let the kids use the bathroom alone at school and it's a program for 3-4yo (but only a couple hours a day).