Hi, A.~
My oldest and youngest are also 11 years apart (the girls), but there are two (exactly opposite) boys in between. Kids are interesting! (Oldest girl has 3 little ones, now, too; so I'm 'Mom-Mom' X 3).
And our 'baby' (*sigh*) will be 20 this Friday and is leaving Tuesday for Air National Guard basic and specialized training in TX (we're in WV). So we are 'empty nesters.
Anyway, our oldest daughter didn't have any 'addictions' (bottle, blanket, thumb, pacifier, etc). The boys both had colic and were quite attached to pacifiers as babies, but gave them up fairly easily when they started walking. Then came Anita and broke all the rules! LOL (For starters, all the others were born on Sundays -- her on Wednesday).
During my pregnancies and their infancies, I read almost everything I could get my hands on about parenting. I always thought I'd be mortified if any of my kids sucked his/her thumb, but I FINALLY read somewhere that if there's something that gives a child 'security', and we try to take it away, it only makes them feel MORE insecure -- and need it MORE. Made sense.
This youngest started sucking her thumb regularly at about 3-1/2 months, so we tried to handle it delicately (not easy for me -- the steamroller type!) When she got teeth, I explained to her that sucking her thumb was making her front teeth stick out (which occurs naturally in my side of the family, anyway). She sucked her thumb avidly until she started pre-school at 4, then she 'broke' herself. It was cute. She'd lay down to sleep -- conscientiously and purposefully keeping her thumb OUT of her mouth -- but when she'd be about to drift off, it would 'automatically' find its way there. That would jolt her senses and she'd jerk it out. Within a week or so, she was done.
I'd advise you that you ONLY 'advise' her (don't make 'demands') about this and let it her make her own 'informed decision' to stop. The more you pressure her, the worse of a problem it could become. (Think logically and realistically, right?)
I also read in some of the parenting info that, if the need arises, you can cut the security blanket in half. Then in half again, and again until they're ready to give up the last little corner (all this with explanations about how, as they age and mature, they only need it half as much -- an encouragement thing). Of course I've also heard of some kids going off to college with a piece of satin binding of their 'blankie'!
Whatever! Don't sweat the 'small stuff' (and it's ALL 'small stuff')
God bless and happy parenting (and grandparenting).