هوى قلبها/ يهوي بقلبها
It is a figurative expression indicates sudden worry, dismay, fear, shock, etc.
Some current Arabic vernaculars may capture this meaning in phrases like:
وقّع قلبي

It should also be noted that in other contexts it may mean "heart fall in love"
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سابع أرض

literally means the seventh earth. Here, it is a metaphorical phrase to intensify the image of sinking, signifying that the experienced emotion reached its utmost degree where there are no further levels to describe it whether it is fear, shock, dismay, etc.

It is an opposite of سابع سماء/ السماء السابعة
which is used to intensify the image of good feelings, ex., I felt like I was in the seventh sky/heaven out of joy

So, your text means that
Seeing her mother on the verge of death as she was struggling with death throes, her heart sinks to the bottom of her stomach (out of fear/ worry)

or in other words, as death doing... to her mother, it made her heart....

Lexical meaning of someone’s heart sinks

-used for saying that someone suddenly feels very worried, upset, or disappointed (Macmillan)

- Used to express a feeling of sudden sadness or dismay.
When you hear news like that your heart sinks to the bottom of your stomach (lexico)

- to feel disappointed or to lose hope (Cambridge Dictionary)

- used to say that someone becomes sad or disappointed about something (Webster's)

Some other idioms that my help may include
someone’s heart pounds​/​beats​/​thumps (Macmillan)

HTH