Well, about mealtimes, I would stop pushing him to eat. You can't force him to eat, and you are making it a power struggle. 3 yr old will not starve himself (though, he may miss a meal or two -- and that's okay!!). When my 2.5 year old doesn't like what I offer for dinner, I say "That's okay, honey. You don't have to eat it if you don't want to." Which will sometimes lead to tears and "But I want ... (fruit, cookies, etc.)". Then I'll say "Well, honey, you can eat ... after you've had most of the food on your plate. Or you can be done eating now. Its your choice." Sometimes he'll choose to eat, sometimes not. If he doesn't, he just eats more at the next meal. And, his height and weight are both in the 75%. When I first used this strategy, I was really worried that he'd be up at night time, complaining of hunger ... but its never happened!
For discipline you'll have to try something else ... something with stronger consequences, I suspect. For repeated misbehavior at meal times, I'd take away the food. Again, missing a single meal once in a while will not hurt your son. For time-outs, I found that I had to up the ante a bit. Time-out within the same room as me wasn't having any affect ... probably, because my son knew it upset me more than him. Now, I leave the room. Or if my son is just really having an off day, then I'll tell him that he's acting like he hasn't had enough sleep ... and if it continues, he'll have to go back to bed. Really, its just a timeout in his bedroom, but for some reason it has a much bigger impact and most times just the warning is enough to get him to change his behavior.
With misbehavior out of the house, I use as a consequence not getting to go out. This could just be one day where you stay home and say something like, "Oh, I'd been thinking of going to (whereever the kid likes to go ... mine likes the grocery), but last time we went out you did (....). Oh, well, I guess we'll have to stay home until you learn how to behave nicely when we are out. Maybe we can try to go out again in a day or two."
Also, when speaking about his misbehavior, be careful to label the behavior as naughty, not your son! And whatever consequences you do, stay as calm and matter-of-fact as possible. Many kids misbehave simply to see the reaction they get from their parents. Of course, staying calm is easier said than done, but the calmer you are the more effective the discipline, usually.
I'm sure the new baby has something to do with the behavior, but that's no reason to excuse it. In fact, firm but loving discipline will probably ease some of your son's anxiety about the baby.
Good luck!