I think you need a doctor you trust, and one you can talk to if you have questions after spending time on the internet. Your child is 2 and you are in for 16 more years at least of being in charge of medical and dietary decisions. Parenting is going to be hell for you, and you will raise a totally neurotic child, if you don't find a physician you can work with. So if this isn't the doctor for you, find a new one. But don't ignore advice without a sensible pursuit of knowledgeable professionals. Which we are not, even if we knew your daughter's medical history, which we do not.
If this is short-term remedy while you work on her diet and fluid intake, then I wouldn't panic. You seem to be worried about aspiration, but can't that occur with anything? (Or are you going to panic about food and drinks and swimming now that I've said that?)
I think the point about it being petroleum based is worth considering, even though that doesn't seem to be your question or on your list of concerns. (If you use Vaseline or baby oil, even topically, then you may not be that concerned.) There are other oils you can consider and I would go back to the doctor and discuss them. If you want to try medication (as your last sentence says), that's an option but it's not necessarily better for your child than mineral oil or a food-based oil.
There are also foods to use, which can be pureed or mixed with other things, like prunes, prune juice, high fiber foods, most fruits (no bananas) and many vegetables. I would not offer your child junk juices - just water. I would not offer processed foods at all, as they are not healthier for your child than the mineral oil that freaks you out. I think you can improve the fiber content of foods she likes - for example, if you make your own chicken nuggets with a breading made from wheat germ and then cook them in olive oil, or if you make oven fries out of potato wedges (peels on) with olive oil instead of French fries, you'll bump up her fiber and nutrition naturally without needing as many of these add-in products for hard stools. You can make high fiber muffins and you can add a lot of stuff to baking mix for pancakes (I add bran, flax seed, and wheat germ to mine).That's not an overnight fix, and there is a risk (as well as pain) from her current condition, so you need to do something short term as well.
I think you can work with the doctor (this one or another), a really good pharmacist, and a good librarian for good cookbooks for kids that will make meals more fun and more healthy for a kid with her problem.
