How can I strengthen my lower body? I have been trotting with no stirrups. Do I keep doing this or do something else ?

No stirrup work helps an absolute ton in strengthening your core and leg muscles, so you're working on the right path. Working out outside of riding would also be helpful, just target the muscles you're trying to strengthen with the exercises you choose.
Leg works at home help a lot! Annoyingly sometimes we gotta work out to get stronger not just ride. Though I wish I could just ride 😝
Working out at home!! I can give you a lists of workouts for your legs and core
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