I give that context to help you see what I mean that the reason side projects and leet code have taken a back seat to your other initiatives (playing/building a relationship with your kids, time with your spouse, maintaining progression or status quo in your job to make a living) is that you haven't found a way to make it a true priority in your mind.
An analogy I find useful for myself to be honest with my own priorities is to think about your other life initiatives as epics on a Jira board. And during backlog grooming and at the beginning of every quarter and sprint, your team is tasked to re-evaluate competing tasks from different epics - some of which you have committed to at the start of the quarter and need to deliver an outcome by the end of the quarter, and some that are aspirational - like cleaning up tech debt most times. As you know being an sw engineer, some things just end up perpetually in the backlog.
And applying that to family life, with kids, you ultimately ended up with 2 new initiatives, one for each kid (each epic with their own stories and things you'd like to do and you find important). And this, for the first time in most people lives creates a true time constraint because now you can't possibly do all stories for all the epics in your life. So you have to pick and chose wisely.
Emotionally, this is hard to come to grips with and accept - for myself especially on a daily with my strong dive and frustration I can't capitalize on the AI moment now with the speed I wish I could had I not had kids. But in my heart, the Kids epics will always take priority and I derive a lot of personal, non financial, satisfaction from working on them.
So in this framework of thinking of your life ^, you can then begin to do the grinding work of trying to constantly figure out how to do other personally important epics from the backlog by trying to "kill 2 birds with 1 stone" like I try to do by combining kid activities with my backlog tasks - ex. make a morning quiet time routine for the kids to play with each other on the weekends when I have the most energy and clear thought to make progress on ideation and try to think of the next steps in testing my business ideas either by doing or just spending time to think.
This ^ type of constant thinking is only present if you truly value the other epics in your backlog (for you it could be side project or leetcode) and don't find it even more draining to think about. If you emotionally feel drained thinking of doing those tasks, then you won't have clear emotional alignment and as a result, never want to try to squeeze in these tasks into an already fully committed sprint or quarter of epics/tasks related to your family and job.
For many, including myself, leetcode's lack of clear deterministic value to career growth often makes it hard for me to really want to focus on it. Whereas, I have strong desire throughout my life to build a company of my own.
I'll give you an example of how strong my desire to start a company by next year by saying, I purposefully looked for jobs this year that did not prioritize my upward corporate trajectory to director of eng and instead looked for months softly on LinkedIn and just asking around for contract jobs or full-time jobs that paid well (maintained our family afloat and met the requirements of my epic of paying bills) and did not demand more than exactly 40 hours a week where I had to even think about the work during off-hours. And I was fortunate enough to have one show up within 4 months. And now doing this job, I can easily spend 30 hours a week thinking/doing work for that job and now have 10 hours during the week, when the kids are in daycare!, to focus on build.
And as context, a year ago I did not have this strong of a desire because there was not a great new tech shift to make building a company easier, and secondly, I was highly focused on having my 2nd child (our decided last) and just getting him to an age where he could be more autonomous (around 1.25 yrs old I've found for this guy). So my "epic" of starting a company was not a strong emotional desire because the pieces and timing were not there.
I say this in order to maybe help in framing how to make sense of your own prioritization in your heart on these other things you want to do. Sometimes the timing is not right just as it is in the corporate world and why you do quarterly business reviews in Google or other companies to dynamically realign based on the situation around you to make that one initiative seem like it is the right time. If you are a business strategy nut like me, you should read Working Backwards the book for an anecdote on how even Jeff Bezos could not force Amazon Prime to happen. He wanted them to deliver that promise of 2 day delivery but not all the pieces were there and quarter after quarter they tried to "kill 2 birds with 1 stone" by fitting all the pieces needed to make Amazon Prime possible logistically with other immediately impactful initiatives.
This is just to say ^ even in work, companies face the same constraint problem you have with your 3 and 6 year old - they want to do amazing things now but can't because there are 50 other immediately impactful and amazing epics to work on. And depending on how strong a drive there is by leaders to get those done, they can either wither away or be incrementally worked on by trying to "kill 2 birds with 1 stone".
Hope this framing helps you find your drive and filter through your personal emotional priorities to find a productive path forward on your current backlog initiatives of "side projects" or "leetcode for career development or job security"