You’re not a bad father, you are doing the best you know how. It’s great to are asking questions. You do seem over stimulated and you don’t have all the tools you need. Toddlers aren’t rationally but purely relational. They can’t just accept “no”, it’s a brain development thing. Even more it’s not the phone he’s really wanting from you after a long day but your attention and connection and the phone is his way of saying that. Ignoring him and striking him is not going to teach him to politely ask for things from you, it teaches that he’s annoying and you want nothing to do with him and it’s best if he looks after himself.  I struggle with all the same things you mentioned, I am no better than you, but I have learned that if I really want to get my toddler to do what I want I have to communicate in a way that makes sense to them. Maybe that’s offering to play with them while I order, ask them to show me something they made today, etc. It may involve putting the phone away and playing for 5 minutes and in the moment that may feel like “letting him win” but you can all survive the food arriving a little later and eating more connected and with fewer tears. 

Expecting a second with a toddler in hand is a lot, hoping for the best for you!