You poor thing; bad naps are horrible when you've only got one, let alone two plus a toddler. I think you're doing a fantastic job just to keep everyone alive. :)
I had a horrible time with DS's naps at this age too - I think it's very common.
Don't beat yourself up about the crying. Whilst I'm generally in the anti-CC camp, I think you can only do what you can do and frankly, with twins it's about survival and anything else is a luxury.
I think that attended crying is very different from being left on your own to cry. I think there's a difference in cortisol (stress hormone) levels since babies experience less stress when crying with someone there, so the effects of crying are less bad. And apparently babies are especially receptive to touch between 2 and 4 months so the fact that you were touching him will have made a real difference.
It sounds to me like they're overtired by the time you're trying to get them off, especially DT2. Once he's crying with tiredness he's almost certainly been awake too long and will find it hard to go to sleep. You need to start the going-to-sleep process before the tired crying starts IMO.
Sleeping for only 30 mins and then waking up tired is another sign of overtiredness. It's different to waking at the end of one sleep cycle and struggling to stay asleep into the next cycle, because the LO is very unlikely to go back off by any means.
I'd try for a shorter time awake tomorrow if you can. Many babies that age can't manage more than 1.5 hours awake without getting overtired, and some as little as 45 mins. The length of 'happy awake time' tends to increase as the day goes on, so the time between waking & the first nap is usually the shortest of all.
I'd watch for the slightest sign of tiredness from DT2 and try to get him off at the first yawn. It sounds like DT1 was less tired/distressed, so it might be that she can go a little bit longer between naps - in which case you could try getting DT2 off first, then DT1.
That age is really tough as there's a pretty short 'drowsy window' in which it's easy to get them to sleep, and if you miss it, it's really hard work (and they get very upset). That does improve with time, and the window gets longer, but that's not much help to you now.
It's extra tough with non-identical twins because they may not naturally want to sleep at the same time so their sleepy windows may not coincide.
With DT1, could you feed her lying down on the bed so that you have the possibility of moving away? Some people find that putting their rolled-up pyjamas next to the baby helps them not miss your presence enough to wake up.
I'd try a cot nap for the first nap of the day if you can. It's supposed to be the easiest nap one for babies to take as they're better rested after the night & less likely to be overtired.
Another thing which helped me was to have some music / words which you say when they're actually going to sleep. You need to do it first when they're actually just drifting off. After about 3 days they've learnt to associate those sounds with feeling tired & sleepy, so you can sing / say them when you're trying to help them go off. It made a real difference with DS.
I wonder whether your DT2 might be a baby who needs to release tension by crying which would explain the crying before sleep. There's more useful info on the AskMoxie blog on tension increasers / releasers and on putting down a sleeping baby (scroll down a bit to find them). IMO the comments on her posts are always worth a read as well.
If you do need to keep rocking, could you use a rocking chair? I use an Ikea Poang chair to rock DS to sleep in: he's 13 m.o. and 26lbs +, and I don't find it a strain as the chair does the movement for you. It's not too expensive. Another alternative might be something like a baby hammock. At least that would let you rock both of them at once. Or a cot rocker?
The other thing that occurred to me is whether there's any chance DT2 might have reflux? I've no experience of it myself but the crying in the pram but not the sling might suggest something like that.
HTH. I'll have a look at my books on sleep tomorrow and see if they have anything to add about twins.
Hope you have a reasonable night. :)