HOW TO AVOID BRACE OR BTV WHEN YOU TAKE CONTACT

To avoid the horse bracing against the hand and the contact avoid pulling directly back on the reins. Instead lift one rein and ask for lateral flexion. The bend supples the horse and eliminates brace.
Once you have lateral bend, yoou can squeeze both reins to ask for the horse to give poll flexion (but stay bent whilst doing it) and if the horse doesn't come into frame avoid pulling the horse into frame, simply use your voice, seat or legs to tuck the pelvis and drive the horse over the topline into the bridle and onto the bit.
Always follow any poll flexion with a neck extension, no matter the length of the frame. A neck extension doesn't mean "long and low" it means lengthening the space between the vertebrae and keeping the throat latch open. If you for example have a collected frame, you would simply give your elbows an inch forward every few seconds to "stretch" the neck slightly.
To fix Behind the vertical BTV
1. Lift up the nose (bring your hands forward)
2. lift up the withers (bring your hands over the withers)
3. Create lateral flexion
4. Ask for poll flexion with lateral flexion
5. Give neck extension (stretch the neck slightly forward)

[@analdus]

Beautifully explained. I often feel my ride is determined by the first taking of contact.

[@jaynfontain6635]

Try this when they come behind: in a relaxed rhythm, add leg & push your hands forward with the feeling in the hand like you are throwing a sheet over bed. Also, lovely pony :)