It sounds like that your contractual obligation is to let them know about a second role, not an outright ban on it. Is that right? Because that makes quite a difference. If your contract forbids taking any other form of employment then you are clearly in breach and it's a breach that can't be corrected after the fact. If you are simply required to notify them then it's still technically a breach but one where the condition can be retrospectively "perfected" by dealing with the notification.
Even in the latter position your employer may be able to justify giving you a formal warning (because technical breach). You mention that the actual clause is worded confusingly and that might assist you in arguing that it would not have been clear to a reasonable person exactly what the obligations were.
You suspect that this is part of a set up to manage you out because of your pregnancy. You are right to have sought advice from PTS. Have you also tried ACAS?
I think it is relevant that others with paid roles outside the workplace have not been disciplined. This may be evidence of pregnancy related discrimination if it's comparable, which you can raise, but you need to tread carefully. For example, does the condition refer specifically to other employment? It sounds like rugby coaching, babysitting etc would be a self employed enterprise with no employer involved. If so your employer could say those scenarios are not comparable/not in breach. If the wording is wider (ie relates to any other paid work or even unpaid work) then you have a better argument.
If your colleagues' other roles haven't triggered a tax change because they are unofficial/cash in hand, employer may claim to be unaware of them even if advertised and you may have difficulty challenging that unless you can prove actual knowledge. Otherwise manager can just say they will look into that going forward but that does not change your own disciplinary process already in motion.
They've already indicated that the outcome is likely to be a formal warning and you might not be able to avoid that. You won't lose your job but it's a strike on your record which may go against you in future particularly if you don't stay squeaky clean.
Please get some further advice, from an employment lawyer if necessary. What PTS advised sounds a bit "woolly".
Disclaimer: I'm a solicitor but not an Employment specialist.