rescued two 2-yr-old Pom-chis and housetraining

Question
QUESTION: Hi.  First, thank you for your time.  I'll try to be short but thorough.  I know there are a lot of questions about this same thing, but I can't get through a day without an accident, and nothing I've tried is working.

We adopted a 2 year old brother and sister Pom-Chi duo 1 month ago from a shelter.  They've had some training (obvious b/c they can sit, come, leave it) but not sure what was done with house training.  They were fixed just 2 weeks prior to the adoption, and I know marking can be an issue.  However, it seems that the male is doing more than marking, as it's not always the same area, and it's always a full bladder worth.  I am home most all day every day, and crate them when I'm gone and for the night (they do not go in their crate, although I did set up a paper lined litter box in the corner, hoping they'd hit that if the need struck, and they have only once or twice).  During the day, I take them out when I "should" and the male will pee each time, regardless of whether it's only been a short time since the previous time (he'd go every hour if I took him).  There has been times when he'll come in and pee right away (after going) or times where we'll call him to go out and he'll drop and go where he's standing.  Tonight he peed in his bed right in front of us.  It's as if he doesn't get this is not allowed.  What I've tried: "punishing the potty" (trainer advised I get mad at the potty since I can't always identify the dog that peed), rewarding for each success, taking them out early and often.  I even tried tying a sock with a pad around the male (trainer advised) but he's so active it doesn't stay on.  I walk them daily, allow them outside and indoor play time, and have visited the dog park 1-2 times per week.  We just began obedience training.

A thought is that I crate the male, except at times that he is sitting or playing with me, eating, or exercising.  Is that cruel?  I am home, so it seems mean.  Also, since his sister appears to be succeeding at not peeing indoor (we've not caught her anyway) do I leave her out, hanging out with me although the male is crated?

Also, I should note that they were diagnosed with coccidia shortly after the adoption, and both completed antibiotics, which should have taken care of any uti's, I think.

Thank you again for your help.  :)

ANSWER: No,it is NOT cruel to crate the male full time until he is house trained-this is what I recommend and do it for about three weeks. However do not put litter boxes,papers ect in there as you want him to hold it while in the crate and let him outside every 2 hours or so. this really is the fastest way of house training. I don't believe that this is a health issue,this sounds like a behavioral issue. After three weeks you can slowly let him out more,if he starts marking again back into the crate he goes full time for another ten days. As for the other being out,it might be a good idea to block off the area were the crate is so she can't walk past him and cause him to become too excited

---------- FOLLOW-UP ----------

QUESTION: Awesome, thanks for that.  Next: when I do catch the male peeing, how should I react?  How about when I find pee and do not know the offender, do I continue to "punish the potty"?

Answer
You have to really catch them in the act to punish them,as punishing them after the fact won't work-as dogs won't know why they are being punished as they won't remember the accident. If you catch them,the best thing to do is to say 'no-no' really fast and pick them up(since they are small)and take them outside to finish,and even if they did finish this will give them the idea to go outside