As far as the criminal justice system is concerned, a defendant can change his barrister as often as he likes.
However, if the barrister's fee is being paid from public funds (i.e. 'legal aid') you should check with your son's solicitor to find out whether it's possible to make such a change without losing public funding. (It's the solicitor who will have chosen the barrister. He/she will know the details of the contractual position).
A barrister's primary duty is to follow his client's instructions. If the defendant states that he intends to plead not guilty, the barrister is obliged to represent him (to the best of his ability) in presenting the case for the defence. (The only exception would be where the defendant admitted his guilt to the barrister, or to his solicitor, in which case the barrister would not be allowed to represent the defendant when he pleaded 'not guilty').
However a good barrister will examine all of the facts and put those together with his knowledge of the law, court procedures and (very importantly) his experience of the verdicts which juries return under particular circumstances. He will then advise upon the best course of action. That means that he might quite reasonably say "If you continue to state that you're not guilty, then I'll put your case before the jury. But I can tell you that, if I do so, they'll find you guilty and you'll be given a lengthy prison sentence. On the other hand, if you plead guilty, I'll be in a good position to argue for a non-custodial sentence".
What you see as "pressure" might simply be the barrister working in the best interests of your son.
Chris