Opposite parenting style. Rant/advice needed

My friend and I have opposite parenting styles. I'm a teach independence, allow natural consequences, me=parent/them=child, type Mom. She's a cater to every whim, "it's easier if I do It", her=slave/child=queen, type Mom.Normally I don't care. All parents are doing the best they can. We have an arrangement where I watch her daughter(5y) after school until my friend gets off work around 5pm. The results of her parenting style is exhausting me and plucking my last nerve. Seriously. This kid won't/never had to do anything for herself. I'm trying to keep calm but my patience is thin. In the beginning I took time and showed her how to do things. Walking her through step by step (ie point remote at tv. Press red button) I would like to think that since September she has grasped the fact she has to open her own snacks, plug in her tablet, use the remote for the tv, put her outside gear on, walk through the park even when tired, unzip the pencil case to get crayons, use the scissors to make crafts, roll playdoh etc. But no, she constantly asks me to do it. I do not. I encourage her to try, which she refuses. Then I tell her she is capable and if she doesn't do it for herself, she won't have that item. There is usually a 5 minutes stand off and she either does it herself or gets one of my kids(age 4&7) to do it for her. But even they have told her to do it herself and have stopped helping, which has caused a few tantrums from her. I join in playing with the kids a lot, but I draw the line at playing for them.I know that part of my issue with this is because I was raised similarly. My parents sheltered me, did everything for me and when I was thrust into adulthood I was incapable, impatient, insecure and useless. It was a hard steep learning curve, and if I didn't have my husband, I probably would have spent the rest of my life that way. I still struggle with a few things, but I'm now 35 and a strong, capable, independent woman!I want to be a good role model for this girl, but her playing dumb/acting useless is infuriating me. Any words on how I can keep my cool and be a better babysitter? via /r/Parenting http://ift.tt/2sPP7Zc