@Katie L -
I don't think you should beat yourself up about rhythm until you've experienced playing a lot more music. If you had a teacher, you'd probably be playing along with them & getting help with rhythm from the teacher.
The Fiddlerman tutorial video is about as close as it gets to having a teacher!
Use a laptop (or go to YouTube Channel on your TV & search title) to pull up this YouTube video, "A Tune a Week #35" - Song From a Secret Garden Tutorial from Fiddlerman!
You can adjust the speed of the video by clicking on the settings icon, if you need to make it slower - even if watching on your TV.
You can right-mouse click, then click 'loop' on laptop - but, I have NO idea how to loop a TV YouTube Channel video, just catch it before it ends & restart (I hate ads).
I would've never thought to go to 3rd position, because of what notes were visible in Katie's attachment. Do you always make sure you don't use open strings?
Thank you for sharing that!
I'd also consider 4th if there are not a lot of G's around.
Depends on how crucial/difficult it is to find and correct the C# (if it's slow, you might want a more emphatic C#). Sometimes the pinky is too much of a risk for this.