With time and patience and proper handling, you can socialize almost any horse. With the info you provided I would be more likely looking into getting the younger, friendly miniature.
What are your actual plans with the miniature? at the age of 11 your daughter is already going to be big for the pony. Is he/she going to be cared for as a companion horse?
To me a horse with a good personality and temper will always beat any perfected conformation, especially in this case. Though you can teach and retrain a horse to be quiet and confortable around people, you can't teach to have a naturally friendly personality which is why I say I would personally always choose a horse who naturally shows curiosity and friendlyness towards you. A horse who asks for human attention. Again something that sometimes happens when you spend time with horses, but a lot of time also doesnt.
As posted above, taking a look at the dam is going to tell you a lot about the miniature. Foals spend the first big portion after birth, with their mother. They will play and learn from their dam, so if you have a dam who's sour and hates people, hates other horses, hates the world in general-you can make a good general assumption that you might have a foal who is also going to reflect that for temper just because thats all their around.
I used to breed miniatures and I had this outstanding mare who had the most unfriendly temper. I also had 2 other broodmares who were the complete opposite. General speaking, her foals had a tendency to be non-chalant. With lots of handling and early weaning it was never really an issue. Almost all of them except for 2 went to become children's ponies. The other showed and became broodmares.