Hi - thanks for your post, story and question - they are good ones!!
Years ago, during my active asthma years, I did go snorkeling - not in a lovely place (like Aruba), but, right here in the New York area in the Atlantic Ocean! Going out past the breaking waves, the ocean was more calm. I donned the equipment and swam below the surface. I had no issues!!! I say that because I specifically recall my asthma was in remission and my breathing was not troubled. In those days, too, I ran track with no issues. Of course, I always had an inhaler with me (just in case), but everything went well (for me!). I say this because, naturally, the decision is yours. You have shared that you have severe asthma and are concerned about being SOB should you get caught in a strong current. As well, you have told us you feel you are not in good physical condition.
I realize you do not want to disappoint your daughter. Perhaps you would consider 'testing the waters' so-to-speak - seeing how you do and feel venturing into the water where you have maximum control. You could see how it feels for you to be in the water, where you can stand, test out your swimming strokes and evaluate how your breathing feels.
What do you think?
Leon L (author/moderator asthma.net)