As an adult who experenced 'tough love' over food - being force fed, being kept at the table until I ate it, being served the same plated meal over and over, being slapped if I spat it out, being made to hold my vomit in my mouth and swallow it again.....
DONT DO THIS.
Don't even do a milder version of it where you bargain and bully the child into having 'just a bite then you can get down' - do you know what that does?
Firstly it makes being at the table an aversive experience.
Secondly, the reward there is relief, and is associated with going AWAY from the table.
So you're doubling down on making the table and mealtimes a vile nasty thing AND making 'away from the table' associated with relief and comparably, good things.
Offer food you know they will eat - bung dinner and any dessert on the table.
Offer a selection of foods they might like - on a different plate.
Say nothing. Not a thing. Not a word. Zip it. Shuttup.
Let them eat what they want of what is there. When they say they are full let them leave the table.
If there are left overs that are salvageable then that is what is offered should they be hungry later, as long as there is still something you know they consider safe and will eat of course. So if they do need another go at it, same deal, set out plates, put food out, leave them to it.
A someone mentioned up thread, it takes many, 100, more maybe for some, instances of seeing that food, touching it, sniffing it, licking it, feeling safe to taste and spit out, feeling safe to explore it, and then actually eating it multiple times, before that food is really SAFE.
Some foods will only ever be 'iffy' and will be accepted sometimes and not others - thats fine, thats ok. Some days I can eat bacon, some days I will vomit at the thought. It's not that much of an extension from some days you fancy a particular food and some days you don't, its a touch more extreme but not TOTALLY out there!
And as others seem to have picked up on...
GRATING food into a sauce is not hiding it. Blend, buy a stick blender or nutribullet type blender and use it. If they can see the veg in there, it isn't hidden is it!
With a bullet or stick blender you can hide mushrooms, courgettes, carrots, lentils, peas, beans, sweetcorn - as long as you don't go so crazy on it that you change the texture, you can hide a LOT of veg.
The only other thing I would add is to let your children see YOU eating properly - again, don't discuss it, don't offer any, just eat. properly. in front of them.