As it is your late husband's specific share of property, you are very much entitled to a one-fourth undivided share in his estate in intestate succession, according to the Hindu Succession Act.

You ate entitled to one fourth share in your deceased husband assets 

You are one of the legal heirs of your deceased husband hence you are entitled as a right to an equal share out of the properties left behind by your deceased husband as one of the successors in interest to succeed to his estates. 

She will only have rights to her husband share 

Yes, under Hindu succession law, you are entitled to an equal share in your late husband’s portion of the property. Once your father-in-law’s self-acquired property was partitioned and your husband received a defined share under the 2003 compromise, that share became your husband’s separate, self-acquired property. When he later passed away intestate in 2018, his property did not devolve by survivorship but by succession under the Hindu Succession Act, 1956.

As per Section 8 read with the Schedule of the Hindu Succession Act, the Class-I heirs of a Hindu male include the widow and the sons. Since your husband died without a will, and he left behind you and three sons, all four of you fall in Class-I and succeed simultaneously and equally. Therefore, your husband’s share in the property will be divided into four equal parts, giving you 1/4th share, and each son also 1/4th.

Your residence in the UAE does not affect your substantive rights, because the applicable law is determined by the religion of the parties and the location of the immovable property (which, if in India, is governed by Indian law). In short: yes, you are legally entitled to an equal 1/4th share in your deceased husband’s portion of the property along with your three sons.

Yes. After your husband's intestate demise, his natural legal heirs under Class 1 are his wife (you), his children (three sons), and his mother (not sure of her status here). Accordingly, all of the surviving legal heirs will have equal share in his properties. 

Yes, you are entitled to 1/4th share in your deceased husband's share of the property alongwith your three sons under the Hindu Succession Act.

Yes absolutely 

Yes. You are legally entitled to an equal share (1/4th) in your deceased husband’s share of the property, along with your three sons.
Here is the legal position clearly explained in light of Hindu succession law and the facts you have stated:
Nature of the property
The property was originally self-acquired by your husband’s father and his brother, and after partition it became the absolute, separate property of your husband’s father. It never retained the character of ancestral/coparcenary property in the hands of your husband.
Effect of the 2003 compromise decree
When the partition suit filed by your husband’s brother was settled by a compromise memo, the shares allotted to your husband, you, and your children became separate and definite interests, crystallised by a court decree.
From that point onward, your husband’s share was his individual property, not joint family or coparcenary property.
Succession after your husband’s death in 2018
Your husband died intestate in 2018. Succession to his property is governed by Section 8 of the Hindu Succession Act, 1956.
Under Section 8 read with the Schedule, the Class I legal heirs are:
Widow
Sons
Daughters (if any)
Since your husband is survived by:
You (widow), and
Three sons,
there are four Class I heirs in total.
Share of each legal heir
As per Section 10 of the Hindu Succession Act, all Class I heirs inherit per capita and equally.
Therefore:
You are entitled to 1/4th share, and
Each of your three sons is entitled to 1/4th share
in your husband’s share of the property.
No exclusion or reduction of widow’s share
There is no legal basis under Hindu law to exclude or reduce the widow’s share merely because:
the property was earlier partitioned, or
the sons are male descendants, or
the widow had already received a share in an earlier compromise.
Once succession opens on the death of the husband, the widow’s right is independent and equal.

Yes, you are fully entitled to 1/4th share in your deceased husband’s portion of the property, exactly equal to each of your three sons. This position is firmly settled under the Hindu Succession Act and supported by consistent Supreme Court and High Court jurisprudence.

You are legally entitled to an equal share.

Since the property became the separate and self acquired property of your husband... your husband died intestate in 2018, his share devolves equally upon his Class I legal heirs.. namely you (widow) and your three sons.

Accordingly, you and each of your three sons are entitled to one fourth share each in your deceased husband’s share of the property...

Dear Client,

 
Since it was his own acquired and separate property, it ceased to be an “ancestral” property on partitioning and distribution among his heirs from his brother. Now, since your husband passed away in 2018 without making a will, his share of specific property is governed under Section 8 of the Hindu Succession Act of 1956. Since you are his widow, you are included as a first-class heir and on an equal footing with his other heirs, i.e., his three sons. The first-class heirs possess equal shares of the property simultaneously. Since your share of the estate is 1/4 of your late husband's share, you will receive 1/4 of the estate, and each of your three sons will receive 1/4 of the estate. Since there is a decree from 2003 settling all matters related to the estate and how each of the members of the family possesses an equal share of the property, and since you are the legal surviving partner, all complexities notwithstanding, you will get an equal share.

I hope this answer helps; if you have any further questions, please don't hesitate to contact us. Thank you.  

- YES, You are entitled to get equal share 

Your understanding is perfectly correct.

You are entitled to 1/4th share in all the immovable properties left behind by your husband as he has dies intestate.

The Hindu Succession Act, 1956 clearly provides for equal distribution among all Class I heirs. As the widow of your deceased husband, you stand on equal footing with your three sons in matters of succession to his property. Each of the four legal heirs (yourself and your three sons) is entitled to receive 1/4th share in the property that belonged to your husband at the time of his death in 2018.

This succession right is automatic and vests in you by operation of law upon your husband's intestate death. The share that your husband received through the 2003 compromise decree, being his absolute property, would now be divided equally among all four Class I heirs.

When your husband passed away intestate in 2018, his property (including his share received through the 2003 compromise decree) would devolve upon his Class I heirs under Section 8 read with Section 10 of the Hindu Succession Act, 1956.

The Class I heirs of your deceased husband are: 1. You (his widow) 2. Your three sons

According to Section 10 of the Hindu Succession Act, 1956, the property of a male Hindu dying intestate shall be divided equally among all Class I heirs, and they shall take simultaneously. In Your case four Class I heirs in total (you and your three sons), each heir is entitled to an equal share of 1/4th (one-fourth) in your deceased husband's property. You are entitled to an equal 1/4th share in your deceased husband's share of the property along with your three sons under Hindu succession law.

So execute appropriate legal documentation, including a family settlement deed or obtain a succession certificate, to formally record and establish your respective shares in the property for purposes of mutation, transfer, or any future transactions.