My second was a bit like this. Low point was when she woke every twenty minutes at night. Jesus wept I can still remember it now - I also had a 2 year old.
She didn't nap unless in a sling. She was very wriggly. And grumpy all the time! After ds we didn't bother with a pram for dd and she lived in the sling all day until 3 months and then I could put her down for short bursts then she'd was in a reclining pushchair.
She actually had quite a severe tongue tie which took 3 months to get a diagnosis. Because she was feeding and putting on weight, no one believed anything was wrong but I just bloody knew there was. Especially as I'd had to deal silent reflux with my first so knew that when I was ignoring my instinct because others said it was fine - I was right in the end.
Both silent reflux and tongue tie are really hard to deal with. I spent hours reading symptoms then not being sure because they didn't have them all.
But with ds, silent reflux clues - he was wriggle but winding didn't help. He did bring up clear liquid, he slept better on his left side and much better once he was on his front (he flipped himself over one night at about 6 months and slept for hours the first time he did it). He had very good head control. He went on feeding strike at about 4-5 months and point blank refused to feed. That was the worst, absolute worst moment of my life as a mother as it just happened one day. Turned his head away from me 
With dd's tongue tie, she was also very wriggly, she used to slip off the boob and make a funny clicking noise, she never seemed fully satisfied, she would need winding after every single feed. Especially at night - that was tough because I'd think she was fine after a feed and put her down. Low and behold she would wake again after 20 mins or so without fail if I did not wind her. Winding her was a massive effort and had to be done in a certain way.
At 5 months dd became a champion napped simply because, I got so fucked off, I started putting her on her front in desperation in the day despite worrying about it massively (she could already crawl by then and had brilliant head control).
The only thing that stopped me going completely insane was that I knew it would get better (ds was a shit sleeper as well). But I came close! I used to have to go to bed with dd sometimes just to survive.