He exited ihram before completing ‘umrah, then he came back a few days later and completed it

Firstly: 

It is not
permissible for the one who has entered ihram for Hajj or ‘Umrah to exit
ihram or stop doing Hajj or ‘Umrah before completing it, because Allah, may
He be exalted, says (interpretation of the meaning):

“And
perform properly (i.e. all the ceremonies according to the ways of Prophet
Muhammad صلى الله عليه وسلم), the Hajj
and ‘Umrah (i.e. the pilgrimage to Makkah) for Allaah”

[al-Baqarah
2:196]. 

If your father
is able to go back to Makkah and complete the ‘Umrah for which he entered
ihram, then it is obligatory for him to do that, and he cannot exit that
ihram except by completing it, so long as he is able to do that. 

But if there
is any genuine excuse that is preventing him from completing the rituals,
then in this case he is muhsaran (prevented), so he should offer a sacrifice
in the place where he could no longer carry on, or slaughter it in Makkah
and distribute its meat to the poor of the Haram, because Allah, may He be
exalted, says (interpretation of the meaning):

“But if you
are prevented (from completing them), sacrifice a Hady (animal, i.e. a
sheep, a cow, or a camel) such as you can afford…”

[al-Baqarah
2:196]. 

Then after
sacrificing an animal, he should shave his head or cut his hair. Then he
will have exited the ihram for ‘Umrah. 

As your father
was not able to complete his ‘Umrah and he went back to your city because he
was sick and is elderly, then in this case he should send someone to Makkah
who can slaughter the sacrifice for him there and distribute its meat to the
poor of the Haram, then he should shave his head or cut his hair. And he has
to avoid the things that are forbidden whilst in ihram until he has done
that, because he is still in a state of ihram for ‘Umrah until he does that
which Allah has commanded the one who is prevented (from completing Hajj or
‘Umrah) to do. 

See also the
answer to question number 37995. 

If he
stipulated when entering ihram, “Allahumma mahalli haythu habastani (O
Allah, my place of exiting ihram will be where You caused me to be prevented
(from continuing)),” then he may exit ihram for ‘Umrah and he does not have
to offer a sacrifice or shave his head or do anything else. 

With regard to
the ‘Umrah that your brother did on behalf of your father, this is a
separate ‘Umrah and is acceptable on your father’s behalf if he is unable to
do ‘Umrah because he is elderly or is sick and has no hope of recovery. 

But if he is
able to do ‘Umrah for himself, or there is hope of recovery from his
sickness, then in this case it is not valid to do ‘Umrah on his behalf. 

Please see the
answer to question no. 41732. 

Secondly: 

When you went
back to Makkah you should have completed the ‘umrah for which you entered
ihram with your father, and you should not have started ‘umrah from scratch,
because you were still in ihram. Hence your second ihram is regarded as
superfluous, and your tawaaf, saa‘i and shaving your head are regarded as a
completion of the first ‘umrah. 

Please see the
answer to questions no. 48961
and 128712. 

If you did any
of the forbidden actions after you returned from Makkah, until you went back
to complete your ‘umrah, then you have to offer a fidyah for each of the
forbidden actions that you committed, unless you did it out of ignorance, in
which case it is pardoned. 

And Allah knows best.