I agree with what Mashi and Shiv are saying about relinquishing control and just giving him the power over his food and his intake. The most popular theory across the board amongst most doctors and dietary experts is one that you have heard before "Children will not starve themselves." YES he may go hungry sometimes. YES he may be THAT stubborn. But in the end, he will eat enough to sustain him as he works through his own mental blocks, cutlery issues, and whatever else is holding him up in the food eating department. It will be hard to watch and hard to not say anything, but the approach they took is probably the one that will end up working best for your LO. It may take a LONG time to get there.....but there is an end in sight.
If you choose to jump into this method of just allowing him to eat what he wants, how he wants it and how much of it he wants......you may find that you want to have (need to have) some go to phrases to respond to him or other people when certain questions arise...like the inevitable things others will mention: he's not eating a lot, he won't try this, he's not using his spoon/fork. And of course the ones he will say, I want more xyz mommy, I don't like this, etc...
I would make sure you are ready to casually defend your approach to daycare with things like "he's a light eater." "He doesn't seem to require many calories." "He's experiencing and adjusting to new food textures." "I pick my battles, that doesn't bother me right now." "Go ahead, let him use his hands, they can be washed."
This way you won't get caught off guard by others and you'll know what you are doing.
In my prior post, I didn't mean to cajole him into eating. I just meant to make it a bit more lighthearted or fun. For the most part, I let my DD eat what she wants and how much she wants. Only on occasion do I encourage her to taste things or eat more of something, but these occasions are when I know she is running off and not eating as much to try to catch the end of a show or to play a game or she is avoiding eating something I know she likes and I know she is still hungry b/c she hasn't eaten much that day or whatever---those nights she'll beg for food later if she doesn't eat enough at dinner) But I KNOW her and she is a good eater for the most part so I CAN push a bit. But the majority of the time, I am fine with what she chooses to eat. I actually ask her what she wants for breakfast and lunch and snacks and she chooses herself most days. I offer suggestions. I decide what to make for dinner and that is the only choice for dinner. That seems to work well for us here.
In any event. I think Mashi and Shiv are right about the approach.
Just saw your post....
I really wouldn't alternate turns with the spoon feeding. I'd really let him do it himself or just not. If you both have yogurt, can you transfer it to bowls so you are both having it out of similar bowls rather than straight from the container? My DH buys those tubs of greek yogurt and puts them in a bowl and adds sugar free jelly. DD now LOVES this as a snack.
As far as his intolerance, IMO, I would really only make foods for family "meals" that HE can also partake in for the time being. As much as possible anyway. I was on an ED while I nursed my son (before he went on neocate) for the same dairy/soy intolerance. Earth Balance was my friend. I found a way to make all my standby meals dairy/soy free. I used panko bread crubs, Earth Balance, almond milk, coconut milk yogurt/ice creams, organic tomato sauce with no dairy/soy for pastas, etc. etc. It was def. possibly to have all my meals be dairy/soy free and not super difficult, although label reading is a pain when shopping. This way EVERYONE is offered the same choices and can be great role models and he doesn't have the "different" from everyone else meal choice. If you need ideas for meals to make with the dairy intolerance that are delicious, there is help for that! I even found brownies I could make with the Earth Balance. Yes they were prepackaged, but they were dairy and soy free and although not the BEST brownies in the world, they made me feel I could eat like other people and that was SO SO nice.

Might be part of his trouble. He may now be noticing he can't have the same as others and that could be messing with his head a bit.