You leave pens in reach of a small child and you don't expect them to scrible on stuff ? Yabu.
Seriously don't believe you didn't know pens were in your study. Everyone keeps pens in study . ( well those luck enough to have a study ).
Op you sound knacked. But really your a bit harsh with your punishments . She's only little . If you dont ease up on the little stuff ,by the time she's a teen you are going to have one mother of a teenage rebel on your hands.
The key to discipline is age appropriate measures. At 3/4 I'd use "no" , and distraction . At 5 I'd use a time out for a few minutes ,in the same room , perhaps a rug or special chair to sit on. I'd only use a different room for a much older child (8+) .
Lower your expectations of how you expect a child to behave...mostly they are just curious and things they do are not deliberately naughty.
Best thing is to look at your home from a child's point of view. Anything you don't want them touching or getting into mischief with , move out of reach or lock up. Tantrums ignore , unless they begin to hurt themselves. Kids soon Learn not to bother if it doesn't get them attention.
I also find most kids will do anything for a sticker ....reward with a sticker for every hour if playing nicely being good. Mine like to help ...when I do housework , to stop them wrecking the rooms as soon as I've done them ...I give them a fluffy duster and ask them to help ...tbh they are crap at dusting but it stops the carnage.
.
Droves - mums of 5 step mum to 3 ( that's 8 , if I can control 8 , including one with asd and one with ADHD , you can cope with baby and toddler. Have some confidence in yourself ).