in my Ukulele Boot Camp I suggest that rhythm and strums would be the LAST thing to work on when learning, especially as a beginner, to play the uke to accompany yourself singing.
Why the last thing? Because strumming and rhythm assumes that you already know the Melody, the Lyrics, and can do the chord changes smoothly in time with the tempo of the song. Once you have those variables down, cold, you can begin to experiment with the rhythms you hear and feel and the dynamics of loud or soft playing, slow or faster strumming.
I agree with those who offered suggestions in your other post that perhaps you're biting off more than you can comfortably 'chew' at this time. While California Dreaming is a beautiful song with a haunting melody, it is also not the easiest song to learn to play. Keep at it, by all means, but also work on simpler, less challenging songs to build your reperatory or treasure chest of songs.
There is a learning curve which can be steep, especially if you choose songs and styles that, while impressive, demand a level of skill and sophistication that beginners need to practice to develop. There is a saying in the science and art of Teaching (pedagogy) which goes: you cannot impart what you do not possess. It applies to performers as well, in the sense that if the performer (teacher) does not possess (has not mastered) the content of what they wish to convey/impart... it won't, yea, can't happen. the desire might be there, but it still won't happen.
It's like vaguely remembering a joke and desperately wanting to share it, but not having shared it before, and only remembering parts of it... any attempt to 'tell' it could be catastrophic
Not to say that your playing is 'catastrophic'...
keep uke'in', we all want you to get 'there'... and have fun doing so!
PS I'm trying to learn James Taylor's/Carole King's 'You've Got a Friend' and my first order of business is to learn the song (cold) without even picking up my ukulele. I think I'm more of an Auditory Learner and I feel the need to have the song (melody and lyrics) in my head/memory so that I can work on 'fitting' the lyrics and the suggested chords into the way I will probably be singing the song (as a performance). Without a full familiarity with the melody and lyrics I will not even attempt to 'play' a song, as I don't 'know' it yet.
At song circles, I'll strum along and listen intently, but I generally don't sing songs I don't know. Learning songs takes time, and learning to play songs or to accompany yourself (and others) singing those songs, well it can take even more time & practice. But it's worth it, as you'll find when you finally play California Dreaming!