I am in a dilemma about responding:
Part of me says, well done getting the relative out for a hunt!
Part of me wonders if more time on the range is needed to experience recoil and how to "hold on".
Part of me wonders how much physical effort is required for the hunt - stand or stalking.
Is the problem a lightweight rifle under recoil versus a heavier one.
Some stocks are less comfortable when fired. (I've shot a Garand in a plastic Ramline stock that felt more supple than good ole' USGI walnut.)
Another part of me asks, will the terminal ballistics be sufficient for an ethical one-shot kill.
I don't have all the answers.
The easiest way out of your dilemma is to take into account that the OP is dealing with a youngster.
The quickest way to turn off a young shooter is to force them to shoot firearms with more weight/recoil than they can comfortably handle at that stage of their lives.
You mention more range time. Great but more range time, practising hold techniques till the cows come home turns into pure misery for a young person that's recoil sensitive and they get turned off the experience very quickly, likely for life.
Whenever I come across a knuckledragger that brags and laughs over the results after giving a youngster or inexperienced shooter his single shot 12ga, loaded with a heavy 3in magnum load for their very first shot with a powerful firearm, I want to take that shotgun and wrap it around the solid bone that should hold a brain.
No, I'm not accusing you of that at all, from your reply, you've thought this through on a sensible level.
In my experience with young people, if they're not enjoying shooting a particular firearm at the range, they most certainly won't be happy hunting with it.
Any firearm that's capable of taking a Deer cleanly at 200 yds is going to produce enough energy that will transmit felt recoil to the shoulder of the shooter.
OP, good on you for trying to keep your daughter interested and unafraid of the firearm.
Most parents that teach their kids to shoot consider this but the one big mistake they repeat time and time again is to teach their kids to shoot on firearms that aren't designed for ''small people''
Felt recoil tolerance is something that can be ''taught to handle" but it never becomes pleasant and almost always develops a serious "flinch" issue for those who are sensitive and it can be extremely difficult to fix. Especially if the same beast that hurts them keeps being used.
Small people need a firearm that fits them well at their present stage of growth. This is one of the biggest felt recoil eliminators to start off with.
When a young person or any person new to shooting is given a firearm that fits properly, with proper drop at the comb and length of pull, felt recoil is minimized. Add a good recoil pad and it usually comes together.
Starting with a cartridge that generates enough power to do the job and with a lower noise level at a recoil level that isn't overwhelming isn't that difficult.
It becomes difficult when that cartridge is chambered in a very light, short barreled firearm.
Muzzle blast is every bit as disconcerting to a new shooter as recoil.
Sooo, I haven't answered all of your questions and maybe even thrown a bit more into your dilemma, but those fine little Howa 1500, short action rifles are reasonably priced, can be had with removable spacers for trigger pull and are well balanced for handling. They're chambered for several light recoiling cartridges that are capable of doing what you need and when the person starts to gain stature as well as confidence, the spacers can be add accordingly.