I truly believe that it's a mixture between prioritizing and finding the right channels to utilize what little spare/free time you have left to promote your blog.
Posting 2 or 3 times a week is great schedule. Especially for a mommy with 2 young ones! Props to you for juggling so much
You'll notice that as time goes on you'll get quicker at writing posts, editing pictures, posting to social media channels, etc. It takes times but that process will speed up--it does for everyone.
When it comes to promoting your blog there are many channels and ways you can choose to do so. Many of the popular techniques include promoting on Facebook by sponsored posts or boosting posts, targeting similar twitter users on Twitters advertising platform for more likes, Pinning to boards on Pinterest, etc.
You can also create Google Ads, Bing Ads, display and retargeting ads but this is a bit more technical and advanced and typically not for your average blogger.
Over the years I've seen a lot of success when I blogged and with current customers of mine at Mommy Host who create content that adds value to the reader's life. With a smaller reader base if you can create content (tips on how to blog more effectively, ways to how to optimize your blog, offering a free guide on how to start a blog, etc) then your current readership may help you in promoting your blog by sharing your content across social media channels for you.
This helps you save time where you don't have to focus so much in trying to promote your own stuff during your spare time.
Additionally, you can reach out to other mommies and ask if they'd like to share your post or if you can guest post on a particular topic to get visibility to their reader base.
It all takes time and patience.