Is my guess correct about analyzing this sentence by grammar?
1.The home improvements have taken what little there is of my spare time.
Question:
Could you tell me the structure of the" what little…" by grammar.

I understand the sentence this way:
The home improvements have taken what little there is of my spare time.(original)
=
1.The home improvements have taken what little time of my spare time there is.(my guess)
2.
The home improvements have taken my very less time , such "little " refers to the "little time" for "there is a little time of my spare time".
which is correct the 1 or the 2.?
Apparently , though the sentence by my guess is not concise.

Is my guess correct about analyzing this sentence?

Question

Is my guess correct about analyzing  this sentence by grammar?
1.The home improvements have taken what little there is of my spare time.
Question:
Could you tell me the structure of the" what little…" by grammar.

I understand the sentence this way:
The home improvements have taken what little there is of my spare time.(original)
=
1.The home improvements have taken what little  time of my spare time there is.(my guess)
2.
The home improvements have taken my very less time , such "little " refers to the "little time"  for   "there is a little time of my spare time".
which is correct the 1 or the 2.?
Apparently , though the sentence by my guess is not concise.

Is my guess correct about analyzing  this sentence?

Answer

Hello Song!
I agree with Duncan but I would like to add that to say "what little there is of my spare time" is the same as saying "the little bit of spare time that I have left". So the writer is saying that: "Doing the home improvements have taken up the little bit of spare time that I have available." which is a better and more natural way of saying it - rather than: 
1.The home improvements have taken what little  time of my spare time there is.(my guess)
2.The home improvements have taken my very less time , such "little " refers to the "little time"  for   "there is a little time of my spare time".
I hope that helps!

Answer

The sentence means that they do not have a lot of spare time - outside of work, sleep, looking after kids, chores, etc - and that doing the home improvements has used up the rest of that available time. They have no time left in the day to do anything now.

You can't say "my very less time". You could say "the little time I have available". 
Less is used for comparisons: "I have less time than before"
Use little to say that you do not have much / a lot.