Trying to get the right look and /feel is always tricky. Particularly when you are aiming at two different demographics ie parents/educators on the one hand and kids on the other. The problem with going for a kids focussed style is that using basic colours can look amateurish.
One important thing is to check that your colours truly do go together. You can check a colour scheme here https://www.color-hex.com/ Here are the recommended triadic colours to go with the pink you have used.
Another design issue is the use of fonts. Again you have gone for informal “child-focussed” fonts. It might be good to experiment with a slightly more normal font for some sections of the site. You need to make sure that you use fonts that work together. Choose a font and then Google “what font goes with …” for some ideas.
Logo. On the desktop version it’s a bit stranded in the middle of a pink background. Also it might be nice to have a “character” in the logo. Something like the hippo in your first video. This then starts to give you a more recognisable brand.
I would use a WordPress plugin to get rid of the post date and author of individual posts
Do you have a Facebook page? If not it’s worth getting one. I think Facebook could be a great traffic source. Setting up a Facebook page is dead easy. Although technically it may be against Facebook ToS you could also set up a new Facebook account separate from your personal account. Then join loads of educator/parenting/kids resources/local pages. Then get loads of Facebook friends (even if they are not friends don’t worry). Based on your first few friends Facebook will keep suggesting more. Obviously aim for people who look like they may be interested in your service but don’t be too discriminating! Then invite these people to like your page. Then every time you post something new on your Facebook page eg a new video or a special offer it will show up on the news feed of some of these people. You need to work at this and keep adding content to your facebook page but it could be useful.
Have you done any songs/vids on the topic of “lockdown”. With a bit of luck and using the right marketing you could get some success from this. So you could post in places like here https://www.facebook.com/groups/1936504910007118/learning_content/
At the end of the day one of your best marketing tactics will be to achieve brand awareness.
Also add a button to your home page to link to your Facebook Page (and also your YouTube channel?)
Are search engines going to be a major source of traffic. If so you need to to do some basic SEO. This will include getting inbound links and ensuring that you use good title and description tags and good use of keywords on your site.
If you haven’t already done so sign up to Google Analytics and Search Console. These will give you valuable info for the future as to your popular pages and how people find your site.
I think at the moment you monetise through ads on your videos and through people buying personalised videos. You could look at using adsense or Amazon on your website as well.
Finally. I hope the above is of some help. Use or ignore whatever you like! Another final thought is you could offer personalised videos from kids to grandparents or grandparents to children particularly sending love during the lockdown. If this feels too exploitative you could offer them for free as a brand creating/awareness tool.