Hi
1) It appears that the father who had 4 sons had done a partial partition to the effect that 2 sons have been excluded from Hindu Divided family and 2 sons continue to remain in HUF. So technically the father has effected a partial partition vis-a-vis members , where some of the members have been excluded (by partition) and other members continue to be the members of the family.
2) Severance of the joint and undivided status of an HUF can be brought about by a partition either initiated by the Kartha or by all the coparceners together and in your case, since it is a partial partition, the consent of 2 sons who are excluded from HUF is mandatory either by way of family settlement deed or registered partition deed.
3) Now that partial partition is in place, the excluded 2 sons should be able to demand and obtain their share of properties (in a definite and specific form) for purposes of disposition, independent of wishes of the former co-sharers.
4) If family settlement deed is not possible, the 2 excluded sons can issue a legal notice of separation or a press notice of separation from their father's HUF.
Hope this information is useful.