Hugs hun, sorry to hear this morning has felt so awful. It is really early days sweetie, and I think you need to do what feels right to you. If you think you'll feel less anxious accepting that their sleep will not be good yet and going with the flow like DH suggests, then why not. I know lots of other reflux mummies have said they've done just that and then have worried about routine later on. If you feel better at least trying for a routine, so you know where your day is going, even if they short nap then that sounds like the best route.
I found once I let go of worrying about sleep with E I did relax more even though she didn't sleep any better. And even if your two are not uncomfortable the vomitting will be disturbing their sleep, and certainly adding stress for you.
Do you feel that you could try the routine for a few more days to see if it makes a difference?
The main reason for tryin to get better naps was the crying mainly at wkends. During the wk they're more settled so not sure what to do for the best.
This makes me wonder whether routine might be the way forward, presumeably you are more on a routine as a family during the week with O at school and DH at work - or perhaps they're a little more stimulated with O at home at the weekends and need shorter A times then?