Can I give you some advice?
My dd is 2.6 and has had access to a pony as we have a shetland and my horse at home.
She has sat on the pony since she was a year old and is now capable of sitting by herself whilst I lead the pony (totally trust pony)
Being brutally honest she lasts about 3 mins! and wants to walk
They have the attention span of a knat.
She only grooms for about 2 mins and mucks out for maybe 3 mins
DD could ride every day if she wanted, but has prob ridden her pony 4 x this year.
I dont push it aas I am sure once she is older she will be more enthusiastic or not as the case may be.
Many of my friends children where exactly the same and now they are older are fantastic little jockeys.
Pony club will take the at 3 I think, but they get nothing out if it, the mothers get more pleasure imho
Wait a few years, go horse riding alone and enjoy some me time- thats what I did till I fell pregnant again