The epitaph you have is written in elegiac couplet, a poetic form where lines of hexameter and pentameter alternate.
Metric poetry can make the syntax a little wonky, so we should not expect clear prose.
This metric structure also suggests that reading two lines at a time might work — and it does.
In the first two lines the key seems to be fui felix, "I was happy".
The rest is a list of ablatives of respect, indicating in which sense the deceased was happy.
For fluent English, you could say something like: "I was lucky for my origin, beauty, son, wealth, husband, intellect, character, and my spirit."
You got the words more or less right, but I think the structure was a little off.
Identifying the key elements (like fui felix here) gets you started with the right foot.
I would reorder the second two lines like so:
sed cum alter partus et [alter] annus nuptae jam ageretur,
interii cum sobole nondum nata.
but when it was the time of second childbirth and second year of my marriage,
I died with an unborn child.
The deceased appears to be a woman dying at some stage during her second pregnancy.
Therefore alter annus nuptae (lit. "second year of the married woman") is more naturally "second year of my marriage".
If it was a man dying without seeing his child born, I would expect an expression different from dying with the son.
It could be an absolute ablative, but the preposition cum rules that out.
In the last couplet, tristius is indeed a comparative, but a neuter one.
It cannot therefore refer to the deceased person.
It appears to be a comparative adverb: "so that I would fall more sadly".
What did Parca do to this end, then?
She showed her so many good things (tantum bonorum ostendit, with partitive genitive) rather than (potius quam) giving them (tribuit).
That is, Parca was so treacherous that rather than giving good things, she only showed them.
With these thoughts, I might translate the last couplet as:
So that I would fall more sadly, Fate was treacherous enough to show me so many good things rather than giving them.
Again, the key is in identifying the core message and looking at possible interpretations.
A good first question is to see which words might go together, bearing in mind that in a poem they might be far from each other.
Frankly, I cannot quite make sense of your translation of the last two lines.
The way I see translation, you should first understand what is written in one language, absorb the idea, and then express the same idea in another language.
If the translated text does not tell a sensible story, something is (usually) awry.
Your translation feels too word-by-word.
One thing that helps immensely here is reading the couplets as complete sentences, but I recognize that that is hard to guess if you are not familiar with the poetic form.
I hope this did not come across too negative.
I wanted to focus on what could be done to improve your translation — not only with this epitaph, but as a process in general.
Giving an improved translation would not help much, but I hope I could illuminate the process leading to it.
I hope this gave you not only a fish but also some new ideas to fishing.