I dropped DD1s day sleep at 2 because she became really hard to put into bed. Same as your 2yo. She would cry and play up for hours. So I dropped the day sleep and I pop her into bed and wall away and she's asleep in 5 minutes. You probably only need to drop every second day to wear him out. I miss the day sleeps but a good bed time is worth the sacrifice.
Unfortunately we've entered a bad cycle too and she's waking up at 3am and demanding my bed. Still trying to solve that one! I have a new doll I'm holding hostage till she stays all night in her own bed. I've also promised a trip to the shops. Not working yet!! I'm hoping it's like a PP said and they just don't one day.
Rest assured you're not a failure as a mum. I asked my sisters and friends for advice to stop the move to my bed but every single one of them had kids sneaking into their bed during the night.