Don't beat yourself up, and don't let anything or anyone guilt trip you about the TV.
When I was a small child - up to about age 7-8 actually - we didn't have a TV. Mum used to put a pile of drawing paper on the kitchen table for us, and we would draw, colour, cut paper, make holes with the three hole punch, scatter the little cutout circles all over the place, etc. We played outside. We played with our dolls. We played with clay. We made castles with the couch cushions and blankets. We fought like cats and dogs. Mum used to make little yarn dollies for us and let us roll out dough, 'help' with measuring, sieving, and other baking bits, and gave us dusting cloths to 'dust' with. We also read, and she read to us.
Many years later, I had the TV on one day ('one day' - was it ever off???) when mum visited, and she and my DCs spent a few cozy afternoons on the couch watching entertaining children's programmes, singing along, laughing at the funny bits.
I joined them and she said, "God how I wish I had had a TV when you were all younger!"
I loved and still love my DCs, but for the sake of my sanity I needed to start and finish household tasks and admin stuff without 'help', and I figured it was good for them to be bored sometimes, to have to learn to entertain themselves a bit. I don't think there's anything wrong with TV.
Your DCs are at an awkward age, and there is an awkward age gap that makes it hard to find an activity they can all be happy with. They are too young to read or do anything for more than about 20 minutes before needing help finding something else to do. You spend your whole day mopping up wet paint, trying to fish broken crayons out from under the couch, scrubbing marks off walls, washing the table, sweeping up after lunch or washing marker out of clothes. They hit each other, knock each other over, pull hair, shout, yell, complain... It can be very frustrating. Your own work takes ages to complete. You feel your life is like Groundhog Day.
Try to get out once a day, even for a short walk and run around with a ball. Try to spend time alone with each child each day just chatting. After that don't worry.