Firstly OP, you're not failing.
Whatever rules etc you live by in your household, forget them. Start again. Very clear boundaries, firm voice,. Get a time line like they use at nursery, so your DS knows what is happening, and when. All meals at the table, highchair for DD.
When DS is naughty, get down to his level, tell him firmly, no, that's not how to behave.
If he breaks a toy, throws something, take it away from him, put the toy in a box, then tell him if you can't play with something nicely, then you can't have it.
Tell him what you expect of him, you can walk next to the pram, but only if you behave.
Every time he hits your DD, firmly, "no, that's not acceptable".
Get a bog standard clock, colour in when he can get up. Put it up high on the wall.
Praise every bit of good behaviour. Explain simply why bad behaviour is wrong, ie you've opened the door, you've gone out side, you could have been hit by a car, then you'd be hurt", short simple explanation.
Get DS to help you with the dinner prep, or lay the table. Get another chair to sit between DS and DD.
Kids need routine and stability, and all to be treated equally.
Good luck 🤞🏻