Everything depends on the specific circumstances of your daughter and her half siblings.
No one here can give you advice about a legal case that is very highly fact specific.
Having said that, I note that you said:
"There is also a lump sum to be divided between the sibs. The eldest has applied for probate and she will divide this lump sum equally between the 3 of them when it is released on probate being granted."
So, there are three children of the deceased and the plan is to divide the estate equally between the three of them?
In addition to this your DD is also receiving a pension as his dependent.
If you do try to make a claim I would guess that the first question to be answered is what extra support your DD needs that would not be met by having an equal third of the estate?
You have not mentioned any reason why your DD might need extra support. Is she disabled or have some life limiting illness for example?
But, the more usual way of making a claim is under Section 2 of the Act rather than Section 9.
Section 9 deals with things like life insurance policies and cases where the value of the deceased's estate is disputed (for example, the value of the deceased's share of a property is disputed).
So, for example, if a property was owned as tenants in common and the deceased owned 50% of it, that would automatically be part of the deceased's estate. Although there may well be arguments as to the value of that 50%.
But if they were joint tenants then the property would normally pass by right of survivorship to the other owner (typically the surviving spouse). However, Section 9 allows the Court to override the normal operation of the law of survivorship, especially if the property concerned was a rental property rather than the main residence.
It sounds as though there may be a dispute as to what property/ies are included or not included in the estate.
All in all it gets very complicated indeed. You do need very specific advice from a lawyer who specialises in this area. There is a body called the Society of Trust and Estate Practitioners (STEP), these are solicitors who are very experienced in this area. Might I suggest that you google something like "STEP solicitor [name of your town]" which will bring up a list of qualified and experienced solicitors in your area.
You may also wish to google "contentious probate solicitor [name of your town]" as well.