I'm not going to jump on the "find another instructor" bandwagon just yet, there's 2 sides to every story.
I have been known to slap the fire out of a horse who needs it. But to earn a real good face slap from me, they have to have bitten or in some way convinced me that they will be biting soon and generally be acting REALLY aggressive. Since I wasn't there, I won't say the slap was inappropriate but, since I also own 10 horses and can't recall the last time I slapped one all the way to Texas, it probably is inappropriate if it happens frequently.
As for kicking the horse......yeah....I don't like it but I don't necessarily think that in itself is abusive. I don't belly kick my horses, or chest kick them either, mainly because they'd practically have to be a mini in order for my short legs to reach. Again, if it happens a lot, it's probably inappropriate. There are other ways to discipline, better ways.
Slapping a stallion on the penis is an accepted (not by me, btw) way to get them to 'put it away', it's been taught for years. Again, I don't do it, but I can count on the fingers of one hand the number of horse people I know who don't. And they do it to a gelding who gets too comfortable too. I tell my stallion, "Quit it, you're not getting paid." and redirect his thoughts to work and that solves it.
First time posting and leaves you to try it out for 80% of the lesson. She introduced the concept, let you try it out to get the hang of it and at the end let you know it wasn't perfect. So? She probably didn't care if you were on the right diagonal, she just wanted you to get the hang of going up & down with the footfalls. Now that it's been introduced, she can start giving you refinements.
Yelling at the other students....well, if they're like me they tend to get focused and forget she's there. If she wanted my attention she'd yell and probably have to pull me in to the center to get it. If she's not yelling at you, don't worry about it.
Being insulting to the other students. I had a trainer tell me once that I looked like a 'monkey doing something (you insert the expletive) to a football'. Not very nice, but I got the picture (oh boy did I!) and fixed my equitation, PDQ.
And ditto what Chasin' Ponies said about this, " I feel guilt, as part of the human race, for removing them from their natural setting to be given only the choice of labor or death.". I won't even go there.
THIS right here, "I have a lot on my plate right now and my life is a mess," tells me you're in an overly sensitive place right now and probably way over reacting to what's going on around you at the barn. For right now, just concentrate on you and learning to ride. Tune out the other stuff until your own life settles down and straightens out. If, after you're on a more even keel, you still feel she's inappropriate and you're not enjoying yourself then go find another trainer and barn. I don't think she's totally insensitive as you say she's aware of your turmoil right now and has offered you a trail ride rather than a structured lesson. It sounds like she is trying to accommodate your needs right now.