Pretty pony Nina, I can't remember if you've already introduced her to us - whats her breeding and posh name (us NF fanatics like to know these things

)?
Its nice for youngsters to be well handledso they learn to mind their manners and as others have said it can help build a lovely bond of trust, ready for when the 'big scary questions' come later in life.
It is important to remember they are just babies though, and make sure they have a chance to just 'be'

Space to grow and mature, both physically and mentally, are vital parts of a babys' development, especially when bones are soft, skeletal frames are still developing (not usually totally fixed until at least 6yrs, sometimes 8yrs).
Again to endorse what has already been said, lunging a 2yr old should really only be about teaching them the basics, literally just a few minutes (although I personally don't lunge anyhting under 3 and am not a fan generally of lunging). Have you tried long reining, which is really just an extension of lunging but with two reins? This is a gentler way of teaching the horse to move forward confidentally and obediently without the strain that small circles from lunging can put on immature bones.
Ones you and the pony have mastered the art - can be tricky at first and best taught with a helper at the ponys head until you are sure they understand - you can long rein out on walks along quiet farm tracks (or the open forest if you are lucky enough to have easy access). But again, keep it short and infrequent, maybe once or twice a fortnight once you've both mastered the technique?
Spook busting is also fun, and useful for when they begin ridden work) but you can avoid putting too much mental pressure on them by combining this with normal handling for feeding/grooming etc. Again short sessions and not too often.
Sounds like you are keen to get things right with your baby which is a major plus, too many want to rush babies which is sad - why rush them under saddle when you have their whole lives ahead of you. Bit like pushing a 13yr old kid to learn to drive, pass their A levels, get a job, run a home etc. Far better in the long term to let kids of all species enjoy their 'childhood' before expecting them to behave like responsible adults

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