Congratulations, Monster High is a LOT of fun, I'm sure your kids will like them at least as much as you do! The glue problem has sadly been a Problem for Mattel from... like, 2003, I think? All the way to 2017-ish, when instead of going back to chain-stitching or using any kind of glue, they started melting the ends of the hair inside the head. Not my favorite method of securing things, but hey, it's functional and glue-free. I'm actually pretty sure the glues they used were safe, at least for human contact-- the gooey yellow glue from Indonesia (until 2015) is some kind of pine resin glue, while the white glue (from China and from Indonesia after 2015) actually feels like high-temp hot glue.
Okay, so, actual answers to your questions!
In your specific situation, what I'd recommend is using the baby-oil-and-Dawn method on the hair outside the dolls' heads, letting them dry super-thoroughly, then dumping some cornstarch inside the heads to help dry any glue left in there.
Specifically this is because a) I know for sure that baby oil, Dawn, and cornstarch won't hurt your dolls and would have to be grossly misused to hurt your kids, b) I would be SUPER LEERY of using another glue inside the head of a factory-rooted gluey doll, c) I don't know if it will fall out with regular handling by children, and d) since de-gluing Toralei I have had the same problem twice using glue inside a doll's head and I don't recommend it without caveats anymore.
I feel like A doesn't need any real explanation, so.
B) Ordinarily, glues like Aleene's Fabric Fusion are fine to use inside a doll's head to seal a punch-method rooting job. They don't react badly with the vinyl and they're waterproof and wash-proof so, hey. All good there. (Which begs the question of why Mattel didn't use one of those glues, but collectors have been asking that for years.) But on a doll with factory hair you've removed the glue from, I'd always be worried there was a glob of glue or drop of oil trapped in there, having a slow-motion chemical reaction that could take years to show on the outside.
C) The dolls I've used glue on the inside of their heads still have all their hair... but I'm a 40-year-old doll collector who displays more than plays and has LOTS of dolls and several other hobbies, and if the hair fell out in chunks my reaction would be "Oh well, time to do a re-root!" I don't know how they'd hold up to normal play for kids, or how old or how hard on their toys your kids are, so I really can't guess if thoroughly removing the glue would cause balding problems for you.
and
D) So, twice, while scrubbing the used baby oil out of a doll's head, I've had problems with the doll's face paint starting to lift away. Once I was able to save the face with some paint and sealer, and once... well, the doll is clean now and my niece is two and doesn't care if Draculaura has her birthmark or all her eyelashes. I doubt it's the oil itself that's the problem-- I get more oil on the face when I'm cleaning the outside of the doll's head-- but between the oil, the soap, the hot water, and the constant squeezing and agitation, possibly even bits of factory mold-release that didn't get properly cleaned off... Yeah, I don't really recommend oiling inside the doll's head unless it's a doll you can replace if things go wrong.
But hey, that said! Since I mostly just use oil on the outside of the dolls' heads now, I can say that I haven't actually had any cases of recurring glue seepage, not even on the dolls who came to me with the worst glue hair, not even after-- hang on lemme google for a Fahrenheit/Celsius converter-- 38C weather or 80% humidity. Several dolls have even gone through boil perms without fresh glue seepage.
It might only take once, and I'll be honest with you, as someone who could just up and do a re-root if one were needed: a second oil-and-Dawn treatment is still way faster and easier than a re-root.
Re: No glue, will hair fall out?
Okay, so, actual answers to your questions!
In your specific situation, what I'd recommend is using the baby-oil-and-Dawn method on the hair outside the dolls' heads, letting them dry super-thoroughly, then dumping some cornstarch inside the heads to help dry any glue left in there.
Specifically this is because a) I know for sure that baby oil, Dawn, and cornstarch won't hurt your dolls and would have to be grossly misused to hurt your kids, b) I would be SUPER LEERY of using another glue inside the head of a factory-rooted gluey doll, c) I don't know if it will fall out with regular handling by children, and d) since de-gluing Toralei I have had the same problem twice using glue inside a doll's head and I don't recommend it without caveats anymore.
I feel like A doesn't need any real explanation, so.
B) Ordinarily, glues like Aleene's Fabric Fusion are fine to use inside a doll's head to seal a punch-method rooting job. They don't react badly with the vinyl and they're waterproof and wash-proof so, hey. All good there. (Which begs the question of why Mattel didn't use one of those glues, but collectors have been asking that for years.) But on a doll with factory hair you've removed the glue from, I'd always be worried there was a glob of glue or drop of oil trapped in there, having a slow-motion chemical reaction that could take years to show on the outside.
C) The dolls I've used glue on the inside of their heads still have all their hair... but I'm a 40-year-old doll collector who displays more than plays and has LOTS of dolls and several other hobbies, and if the hair fell out in chunks my reaction would be "Oh well, time to do a re-root!" I don't know how they'd hold up to normal play for kids, or how old or how hard on their toys your kids are, so I really can't guess if thoroughly removing the glue would cause balding problems for you.
and
D) So, twice, while scrubbing the used baby oil out of a doll's head, I've had problems with the doll's face paint starting to lift away. Once I was able to save the face with some paint and sealer, and once... well, the doll is clean now and my niece is two and doesn't care if Draculaura has her birthmark or all her eyelashes. I doubt it's the oil itself that's the problem-- I get more oil on the face when I'm cleaning the outside of the doll's head-- but between the oil, the soap, the hot water, and the constant squeezing and agitation, possibly even bits of factory mold-release that didn't get properly cleaned off... Yeah, I don't really recommend oiling inside the doll's head unless it's a doll you can replace if things go wrong.
But hey, that said! Since I mostly just use oil on the outside of the dolls' heads now, I can say that I haven't actually had any cases of recurring glue seepage, not even on the dolls who came to me with the worst glue hair, not even after-- hang on lemme google for a Fahrenheit/Celsius converter-- 38C weather or 80% humidity. Several dolls have even gone through boil perms without fresh glue seepage.
It might only take once, and I'll be honest with you, as someone who could just up and do a re-root if one were needed: a second oil-and-Dawn treatment is still way faster and easier than a re-root.
I hope this helps!