After what Sara said...

You know, If Marisol is mostly for play, you could remove her string and store that string inside of her head, then buy a plastic zip tie to attach her head with.It would be easy to get it on good an tight, and it would be very sturdy for play.Zip ties are very inexpensive and easy to find.You get a lot in a pack, so you could try till you were happy with it.
If/when your daughter wanted the original ties back, you could snip the plastic tie, remove the string from her head, and rethread it using a safety pin.I can see where the zip ties could be more practical for a doll that gets lots of play time in.