My son (now 12 ) was the same, ate everything untill aged 2 then lived on chicken nuggets, potatoe shapes and yoghurt, the health visitors just said go with it, he will change, I did...just let him eat what he liked and gave him vitamins, when he hit 6 he suddenly decided to try new foods all by himself, now he eats me out of house and home. I didn't stress and didn't make a big deal. Now my 4 year old daughter is the same...again started at about 2 and now she will eat only fromage frais, pizza and chicken nuggets, and special k cereal! i give her apple juice to up her fruit intake and figure that she is getting protein, carbs and vits from her cereal.....I'm gonna just sit tight and wait for her to cure herself like my son did.
My daughter has oral aversion (she's had it since almost birth due to being a premature baby and all the tubes in her throat really messed her up there). She also has reflux. She can't eat solids.. just learning now and she is 4 years old. However I've always made sure to get her calories into her; first I was taught (by a specialist SLT) to feed her a formula/fruit puree mix via syringe into her mouth until she was 3.5 years old, now she is on smooth pureed "soups", which are basically whatever we're eating, whizzed through a very powerful mixer (like a Vitamix), with milk and a knob of butter added to make it runny enough for her to swallow.
Since your daughter is that tiny at 4 years old, I'd DEFINITELY push to have her seen by a specialist - are you in the UK, or US? Either way you can have your child seen by a specialist feeding pathologist or speech language therapist specialising in feeding disorders. I'd guess her perforated tongue probably does have something to do with it - our daughter had great difficulties due to having oversized tonsils and things have improved greatly since they were removed last year, but it's still a struggle. I'm certain my daughter will learn to eat properly one day, maybe in a year or so, as she actually enjoys food, but whenever she gets a cold or her reflux meds stop working we're back to fighting over every spoonful again and it really does try our patience.
Anyway, when my DD was young, I also had the advice to starve her which was absolute rubbish - a child that can't eat, or feels uncomfortable eating, will prefer to starve rather than eat. If your GP isn't worried about the fact that your daughter is so vastly underweight, then get yourself a new GP, and demand to see a specialist, Great Ormond Street have a very good feeding clinic if you're in the UK, and they don't recommend starving a child at all - get in touch with them if you have to.
What you can already do though is go with what your daughter can do, i.e. the "pureed slop", get yourself a very high-power mixer, and whizz up everything for her.. add milk until she's happy about the "stickiness" of it, and see if she's ok with that.
Good luck,
Siobhan