Tips for remote work with a toddler and baby?

My wife and I have a 2yo and in a few weeks will have a newborn. My wife is a SAHM. I have a dedicated home office, but WFH has been tough lately. Every time I leave my room, my daughter will want to play and gets very upset when I can’t. She doesn’t understand why I can’t, obviously. By the time I finish work and school for the day, I’ve been hearing crying and whining for 8hrs and am already burnt out. I have noise cancelling headphones (Bose QC45) and hearing protection, but neither one totally blocks stuff out. I’m around my wife and daughter all day every day and it’s starting to get to me. I need some separation between work and home.

I’m seriously considering renting an office space for ~$350/mo, but I’m a little nervous about signing a 1yr commercial lease so I’m holding off on that for now. Working from the local library or coffee shop is a nice change of pace sometimes, but I quickly discovered that doing my job without my widescreen desktop monitor kind of sucks. I’d also like a place with some real quiet, like a dedicated office.

I feel kind of silly paying for an office space when I’m supposedly living the WFH dream, but I really need to change my work situation somehow.