Make sure you tell your trainer about your condition. This is not a time to hide it.
Likely that your personal trainer will not really have any idea of the implications. Possibly they might think they know from very lightweight articles in journals and websites for trainers. Possibly they will confuse types 1 and 2.
So, the likely main point of telling the (inexpert) trainer is to give the context that you have extra reasons to monitor and adapt exercising.
One of the key errors in non-expert advice is confusing the concepts of high intensity ir even high intensity intervals with sustained vigorous cardio exercise activity.
Without now elaborating, the bet thing you can do for youself is keep a journal. Write down the general nature of your session, what you did before during or after (basal bolus nutrients) and how your body responded (even thru the night).
You can be very scientific about this but just start easy and low key as it suits you.
This is the best way to manage the innunerable variations in your training and your body's response. No one can give you a perfect formula, just ideas and things to try. Those who think they can sell you a formula or web based service to manage it are misdirecting you.
Your own management is the key - data, record, analyse responses and adapt (often trial and errors).
In brief, you are "n=1" but can learn from "n=thousands".
As one of those many ideas to trial, i have found that veing ketogenic adapted has made a huge difference. Imagine (on a pimp) vigorously training in the gym or running for 45 minutes or more and still ending up on 4.4 mMol with no basal or bolus or carbs ingested and no nocturnal hypos. Beyond the ken of most trainers, dietitians, nutritionists, endos. (My own records stop their response that it can't be happening.)
Become your own expert in your physical activity.
Best wishes.
Keep posting.