If you give her a treat right after she potties, also, it will reinforce how nice it is to go outside. Take her out at the same time every night and wait
. If she doesn't go within 10 minutes, go inside, wait 20 minutes, and take her out again.
That, along with teaching "get busy" should help (remember to only say it while
she is going for the next few weeks). It is a matter of building the habit of her expecting when to poop. If it's not TMI, my dog poops at 10 a.m. and 4 p.m. (plus or minus an hour or so if I can't go out right at those times).
You can really time it if you are feeding her at a certain time, taking her out at a certain time, and positively reinforcing those outdoor times.
Cleaning the rug should still help, but if she is having an accident because she really needs to go, she'll go no matter what. I'd still suggest confining her at night, if for nothing else than making clean up easier when she does have accidents.
Dogs learn by association and habit. If you are consistent about all of this (taking her out, waiting to make sure she goes, treating, going out at the same time, confining her at night), in a few weeks, you should see a marked improvement.