"The first mitt we purchased was a youth and "easy to break in" it is now too flimsy and possibly too small for the 12" ball."
The "flimsiness" can be fixed by either tightening the laces or replacing them with new ones. I do this service on a mail order or drop-off basis (I'm in Columbus) and you can email me at the address on my profile.
The size of the old glove- that I can't do anything about! But the old glove can be restored to give you several more years of service, used by mom or dad in practice, handed down to a sibling or kept in the bat bag as a back-up mitt.
"Can anyone offer advice in purchasing a mitt?"
My advice is to ignore what someone else tells you is "the best" glove for your child. A glove is a highly personal piece of equipment that should be comfortable to the player using it and inspire confidence in their fielding abilities.
Get to as many sporting goods stores as you can and try on as many different gloves as possible. Find one that fits THE PLAYER and feels comfirtable to HER.
Whichever mitt you choose, try gripping a ball with it to get an idea if it will be big enough. You might want to look for gloves that are ergonomically designed to better fit a female hand.
So you find a mitt that fits well, is comfortable and your daughter loves it. What then?
Well, you can plunk down the cash and take it home, but if you're not in any hurry you can almost always save some bucks by shopping for the same model of mitt on the internet. And don't forget eBay! There are hundreds of deals there on new- and used- gloves and mitts.
"Does cost dictate quality?"
Generally, yes. The more expensive gloves will use all-leather construction and the quality and thickness of the leather will be greater than the cheaper gloves. So, yes, the $150 catcher's mitt will be more sturdily constructed and more durable than the $75 catcher's mitt.
But there again, maybe the $75 mitt is the one that feels most comfortable to the player! Even a mid-priced glove will last for many seasons if it is properly cared for. Keep the glove clean, dry, stored in moderate temperatures and keep the laces properly tensioned and the glove could outlast your daughter's playing career!
What I have found is that amongst the various manufacturers, once you hit a certain price range the quality of the gloves will be about the same. For example, a $150 Nokona glove is just as good as a $150 Mizuno, or Rawlings, or Easton or whatever. The only differences will be the personal preferences of the individual player wearing the glove.
"Is it good to use sprays to break it in or just keep catching balls with it?"
Here again, the break-in method used will be up to the taste of the individual. There are almost as many ways to break-in a glove as their are people breaking-in gloves!
Some break-in methods will get the glove soft fast, but might be damaging to the leather in the long run. Be a bit more gentle and a careful break-in can prolong the life of the leather.
Catching and catching and catching balls is perhaps the best method. Then, when you're done doing that- go catch some more!
But this method can be slow, especially on the more expensive gloves with thicker materials. I have had the best results breaking-in gloves by using leather conditioner which is lanolin based. Lanolin is one of the absolute best treatments for leather gloves.
Use small amounts, concentrating your efforts on the natural hinges of the glove. Better two light coats than one heavy one. Don't over-saturate the glove! It's best to apply the conditioner to a sponge or clean rag, then wipe that on the glove instead of heaping the conditioner directly on the glove. Wipe off any excess and allow the conditioner to absorb overnight before applying the next coat.
Good luck finding that new glove!