A lot of catcher's mitts come my way for repairs- a far higher ratio to fielder's gloves than what you see on the field. I guess it's not surprising, given the pounding that a mitt will take compared to the typical glove. On the field you have, of course, one catcher's mitt among nine players. But I would guess that 1/4 to 1/3 of the gloves I repair are catcher's mitts.
The brands I most frequently work on are Nokona, Mizuno, Easton and TPS. While the Nokonas are more expensive- and deservedly so, based on the higher quality of materials and craftsmanship- the others make some great mitts that are afforably priced. There is no reason that the less-expensive mitts can't last many seasons if they are cared for and properly maintained.
One thing all these mitts have in common is that they have relatively little padding in the palm area to begin with. If you open up a mitt and take a look inside it, you would find little more than a thin piece of felt or leather sandwiched between the outer shell and inner palm. There is little-to-nothing in the way of padding in the sense of the thick padding found around the perimeter of the mitt.
If I was looking for a mitt, I would try to find one with the palm pad feature on the palm lining of the glove, right where the player's hand rests. Those external pads, often made of gel, foam or thicker leather, go a long way toward taking the sting out of the ball.
Other options: If the player really likes the mitt and wants to keep using it, there are several products that can help. Several companies sell pads that can be cut to fit, then attach to the inner palm with adhesive. You can fit the pad right where the catcher needs it and that could be a tremendous help.
If your daughter wears a batting glove under her mitt, there are gloves designed with padding built into them. I have even known some catchers to wear a weightlifter's glove, as they have thick padding to protect the hand.
One more solution is to take the mitt to a reputable glove repairman. The mitt can be opened up to have thicker padding installed in the palm area, then laced back together good-as-new. I've done quite a few of these and the feedback from catchers has been quite positive. The additional padding I add is custom cut to fit inside the mitt and is much thicker than the thin layer of material that comes from the factory.
Besides installing custom padding, replacing worn-out laces can get the mitt back to a like-new shape and form. If your old mitt seems to be getting flimsy or floppy, either replacing any worn laces or tightening the existing ones will definitely solve the problem. You can find more information on glove customization and repair at my website. Here is the link:
The Glove Shop