Get a "car potty." These are life savers!
Go to Amazon, and put in the search words "on the go potty." And many will come up and the reviews.
We have had one since my daughter was that age, and all my friends have one too. It is SO great... and for when there is no toilet, if stuck in traffic, at parks, or anywhere.
I HIGHLY recommend getting one!
For outside pottying... don't rush it. They have to master indoor training... and then their ability for their body to at least 'hold' their pee impulse long enough to get to a toilet. Which in a mall, can take awhile to walk to a bathroom and then wait in line if need be. For example.
Your son, is only in the beginning stages of pottying. He is only just learning. He does NOT have it mastered yet.... so don't force it, nor hurry it. It is a process.... which goes in stages.
He is not yet... at the stage where he 'can' control his bladder outside the home....
I use(d) the 'Potty Scotty" padded underwear, which you can get on sale from Amazon or E-bay.
Pull-ups/padded underwear will NOT confuse the child.... it is a process.... that goes in stages....
When at Daycare... what do THEY suggest? Some have 'rules' on that.
Next, do NOT expect him to potty train for daytime and night time at the same time. NIGHT time 'dryness' is a whole DIFFERENT time-line and process. Night time dryness, is NOT even attained until 7 years old.... because is it a physiological and biological process of the body's organs maturing... and this is NORMAL. For naps and bedtime.... a diaper is still needed.... and no, a child will NOT get 'confused" about that. You simply explain it to him.
Next, pooping in a toilet.... is often a later 'stage' of potty training. So don't force this either. Otherwise, a child can get constipated and the ensuing medical problems from it.
Next, Remember... that even if potty trained during the day time... a child WILL have relapses or accidents in bed. Normal. This is childhood. My daughter wore a night time diaper even at 5 years old, for naps and sleep. NORMAL. AND for accidents... I simply bought 'waterproof bed pads" to put directly under my kids.... which I got from Amazon. It makes clean up REAL easy and I never have to wash the entire bedding/sheets, if/when my kids have accidents during sleep or night time.
My son who is 4 years old, still wears a night time diaper for naps and sleep... because he still wets during sleep. Normal. And per his age.
Don't expect your son, to get it all at once. Pottying goes in stages....
all the best,
Susan