Broken trust potential end of relationship

I think my relationship has run its course.
A few months back my partner lied to me about something that wasn’t worth lying about. Now it has left me questioning what else they aren’t telling me.
Things have never been easy in our relationship between others opinions and various life issues.
Ever since the lie came to light I cannot move past it. I feel the need to invade their privacy and check up on them and while I know that’s not okay I cannot shake it. I am tired of feeling like this, I’m tired of the big blow out fights every six months and feeling like I’m the only one fighting for our family to continue.
We have full custody of my six year old and a baby on the way (too late to terminate even if I would consider it) and the idea of leaving is just as terrifying at this point as staying is.
I’m feeling like for them me still being upset is more of an issue than the actual broken trust and they e outright told me to just let it go and I cannot but I can’t be the only one trying to deal with this either.
It was their mistake and it’s not on me to fix it. Without their help Or at least understanding I cannot see how we’re to move forward