This was one of the reasons I trained Brandi to start using the potty pads. Now she gets up in the middle of the night to use her potty pads. I absolutely love it. Some people prefer that their furbabies only potty outside but for me because of the reasons you just wrote about and cold or rainy weather, kind of force me to trained Brandi to use the potty pads.
For the middle of the night poo, have you tried changing her feeding time?
I am fortunate in that Brandi well potty both inside and outside so she's not confused about where to potty. In the summer, she mainly goes outside. At nights, she will use the potty pads.
It's the greatest thing for me. She will wake up, go downstairs to her potty pad, do her business and come back to bed all without disturbing me. Well actually she does, because she expects me to wake up to lift her back into bed and will sometimes bark to wake me up
. Still better than getting up to let her outside though.