As Argon says, from your description, it sounds like your problems are primarily due to how you're braking... too hard, and too late!
If you're using a wheel and pedals, and you're trail braking, you need to reduce the brake pressure as you turn in... the front tyres only have so much grip, and asking them to brake and turn at the same time will just make the car understeer. The adage to remember is the more steering angle you have applied the less brake pressure you can use. Turn the brake bias down, get most of your braking done in a straight line and for the time being, make sure you have at least a short coasting phase that takes you to the apex... you'll find you have much more front end grip whilst coasting. Once you get this to be habitual, you'll get to the stage you can go straight from the rake to the throttle.
This will also have a positive effect on your corner exits too... the less you're understeering at the apex the earlier and harder you'll be able to pick up the throttle on the exits. If the car is understeering at the apex and you try to pick up the throttle you will either get more understeer or you'll get immediate oversteer. It's the same as for entry... the less steering angle you have applied the more throttle you can use.
If you're using a pad you'll find trail braking more difficult, so get more of your braking done in a straight line and use a longer coasting phase.
It will probably feel slower to you as the car won't be sliding about and you won't have to make as may corrections... but your lap times will be faster
IMO, my set up has a pretty neutral balance and will take a LOT of throttle on the exits, so if you're getting understeer on the way in and oversteer on the way out you're pushing the front too hard. Forget the exit oversteer as that will take care of itself if you concentrate on getting your line and entry speed right.
Good luck 👍