Totally normal to be a little nervous. But don't let that hold you back. You have two qualified instructors telling you to get out there and do it. Listen to them and have fun.
I remember when I went on my first long distance XC. It was a little hot and i had a big climb to get over some...
Nice work. It's always a pleasure to share the joys of flight with someone new...it's even better when you share it with one of your children. Truly the start of wonderful passion.
I agree with Henning.....go up several times a week if possible and use multiple CFI's. I remember learning something from each of the CFI's that I went up with. Something new each time. You're not cheating on the guy that you like and when he comes back or is more available, fly with him...
No problem, let us know how it goes. If it's hazy and you can't find LGB just go direct Seal Beach after the corridor and you'll run into LGB. Don't bust airspace, it gets close over there.
Once you leave SMO climb to 3500 (pretty tough to get there before you go into Corridor) and fly directly over LAX mid field (on the 132 radial). When you get to the 105 you can turn left and follow the 405 towards long beach and call them up on 119.4 for inbound. Don't forget to give updates...
Great story OP. I'll never forget a good pilot friend used to call his final walk around the "Am I doing anything stupid?" walk. I've caught a tail tie down & a step ladder. Both would have been embarrassing situations. Always a good idea.