Sleep deprivation is hard, especially while pregnant. So you have my sympathies. It's a tough one.
When my older kids were small I had to travel for work sometimes. It used to drive me crazy trying to sort out why they could sleep well (at least better) for their father when I wasn't home, than when I was.
In hindsight I have attributed most of these things to being the "safe" one for my kiddos. I have watched as they have continued this, but with other things. They are always more whatever it is, with me. More teary, more sick, more likely to wake. Even now, my children will always wake me if they need assurance at night, never my spouse, ever. He isn't unkind or stern. I believe he is simply less soft & what they are seeking is that. I assume that likely my children did wake when I was not there, but since the one they wanted wasn't there, no sense getting up.
I know none of that helps you to get a child sleeping better. I felt it merited saying though, because I often stressed myself wen my kids were small about what I was doing "wrong" and most of those things just became apparent in time that it was more about the child's needs, temperament & phases than about my mistakes or successes. At least then, I was only dealing with whatever the issue was at hand, and not all my own second guessing or guilt or feeling like I was failing.
The things that help for me most are lots of activity, particularly swimming & being outside. That isn't always possible, so I also had some things to help indoors, like those small trampolines with a handle for toddlers. We also had a bike that had games on it attached to the television, and they had to pedal to make it work.
The goods news is, for me I found tiring out a toddler a lot easier once you have another, because they tired one another better. That isn't instant of course, but as the baby gets to walking, I found that sleep was the hardest when I had my oldest only because he tired me out more than the other way around.
Congrats on the new baby coming.