You must be absolutely exhausted. It's not good for you to eat and sleep so late either. It sounds like you need to do a bit of a bedtime boot camp to completely reset their bedtime routines. Here's what I would do..
Avoid any sugary foods, or anything containing artificial sweetener or caffeine from lunchtime onwards. Start a bedtime routine from about 6pm, with a bath, story and bed. Mine like the Beebies bedtime hour and have learnt to recognise that when the night night sign comes on, they're off to bed.
I'd put them both in any bedroom that's big enough to hold a cot and a bed. Make sure it's completely dark in there, and you have a blackout blind if there's a streetlight outside.
Move any toys out or up high which could distract them from sleep. Get someone in to fit proper window locks if you have any concerns about safety in there.
Put a stairgate (you can get those travel ones which don't need screwing in) at the door. If they can get one open, I've heard of people putting another directly above it so the catch is well out of their reach and it blocks the catch on the lower one. Make sure you can still easily reach it though, so you can get them out quickly in any emergency.
I think the priority is to get them both sleeping in proper cots or beds, rather than swinging chairs, without you needing to go through hours of soothing to get them there. It's nothing to do with not loving them enough, it's establishing a clear routine which will help them feel safe and secure at bedtime. It will also mean you can stay with other people in future without having to go through this at their houses.
I hope this helps a bit. I had to get it cracked as I am evil when tired so sleep was the area I was strictest in. I can't tell you how much it paid off. ds2 is the cheekiest monkey going but never ever plays up at bedtime, or wakes up in the night. I think it's because his routine has never changed, wherever we are, he goes to bed in a cot at 7pm.
I hope this helps, I know it's not easy at all, especially with all you're going through but I do think if you can stick to it for a couple of weeks you will really start to see some results and that will make things easier for you.