Dealing With a Little Stinker

Dog pictured is very similar, but not the same as my mother's dog, Buddy.

So my mother owns this little Bichon that she adopted a year ago from the humane society who was a special needs dog.  At the time he was 5 years old and afraid of everything.  She had to sit on the ground near him (he was opposite corner from her) with her arm on the ground, limp towards him, for an hour before he would approach her.  

Now he is obsessed with her, loves to play with the cat, loves my dad, and thinks of me as "second Carol".

The problem is that he's always tripping my mother and running over her injured toe (I've been trying to get her to consistently tell him to back up onto the carpet, which is the only trick I've been able teach him so far.)  He chases after and tries to bite my brother (my brother is an idiot and it is provoked.  I'm trying to work with him to knock it off the moron) and is afraid of strangers.  He cowers when they come and barks/growls/chases towards the door when they leave.  He never catches them, just does that through the door.  He barks at passers by and will bolt from my mother to chase after and bites the tire.  I wonder if he's been run over by one of those before we had gotten him, because nothing is of greater value than my mother to him.

So what I'm thinking of trying to do with him to correct these behaviors are as follows:   For strangers, there will be new house rules for guests at my parents' house. They don't look at or react to Buddy, sit down, and without looking at him, toss a particularly yummy treat in his general direction every time they come over.  When they leave, Mom is to back him up into the kitchen and get him to stay as they leave.  I'd like many guests to come over so that he is desensitized/delighted by strangers.  They are good things that bring good things.  I'm going to try to get my brother to do the same thing, and will probably hit him if he tries that stupid staring provoking thing that he thinks is so funny.  Yeah, when it comes to Buddy, he's a moron and he wonders why the old poodle we had loved me and bit him, hmmm?

I think that for his fear of bicycles, either my mother, or I should ride a bike nearby in our driveway and the other should have him on a lead and casually walk by without reacting to the bike and do so a number of times and reward him when he doesn't react.  I just don't know who should bike and who should walk.

I'm also going to be picking up some training treats and a clicker I think tomorrow.  I think it will be the simplest way to train him even if my mother thinks that having that clicker on hand is silly. 

What do you guys think?  Anything I should change, modify, anything sound silly?  I try to the Victoria Stillwell methods of training, but I'm a bit rusty.  I taught him the back command months ago when I was in town from MN, and now that I've moved back to WI, I'd like to address these problems quickly and directly before they escalate.

~Lumie