LME does not have anything to do with alpha diversity, unless if you are inputting an alpha diversity vector as your dependent variable. So you can run LME on alpha diversity data, first differences/distances, or metadata values. Trying to compare an LME on alpha diversity data vs. an LME on beta diversity FD data is like talking about apples and oranges — there is no reason why the two should necessarily give related results.
First distances measures each individual's change in beta diversity between each time point. So if you have samples collected from a group of children once per year ages 0-10, then first distance 1 will be the distance between age 1 and age 0 for each child. FD 2 will be age 2 - age 1. Etc. Each individual's sample at time X and time X-1 are being compared to measure FD — there is no "standard" sample that everything is being compared to.
You would need to show me the plots you have for me to understand and explain what you are seeing. It's not entirely clear based on your description.
If you want to exclude certain time points, you need to filter these out. So, e.g., use feature-table filter-samples to remove samples based on metadata values (e.g., age) prior to running LME/volatility.
I hope that helps!