If he does wudoo’ and intends to remove two types of impurity, when should he rinse his mouth and nose?

Firstly: 

Ghusl does
not take the place of wudoo’ unless ghusl is done to remove major impurity
(janaabah, menses, nifaas). Shaykh Ibn Baaz (may Allaah have mercy on him)
said:  

If ghusl is
being done to remove janaabah, and the person who is doing ghusl intends to
remove both types of impurity, minor and major, it is sufficient for both.
But if the ghusl is done for some other reason, such as ghusl for Jumu’ah,
or bathing to cool oneself down or clean oneself, then it does not take the
place of wudoo’ even if one intends that, because when bathing for these
purposes, one does not pay attention to the order in which the parts of the
body are washed, which is one of the obligatory parts of wudoo’, and because
there is no major purification in the intention whereby the minor
purification could be included in the intention, as in the case of ghusl to
remove janaabah. End quote.

 Majmoo’
Fataawa Ibn Baaz (10/173). 

See also the
answer to question no. 82759. 

Secondly: 

Rinsing the
mouth and nose is essential when doing ghusl, as is the view of the Hanafis
and Hanbalis. 

Shaykh Ibn
‘Uthaymeen (may Allaah have mercy on him) said: Among the scholars are those
who say that ghusl is not valid without them (rinsing the mouth and nose),
like wudoo’. 

And some
said that it may be valid without them. 

The correct
view is the former, because Allaah says (interpretation of the meaning):
“purify yourselves” [al-Maa’idah 5:6], which includes the entire body.
The inside of the mouth and nose are part of the body which must be
purified. Hence the Prophet (peace and blessings of Allaah be upon him)
ordered that they be rinsed in wudoo’ because they are included in the
verse: “wash your faces” [al-Maa’idah 5:6]. 

If they are
included in washing the face, which is something that must be cleansed
during wudoo’, then it is more likely that they are included in ghusl,
because purification in the case of ghusl is more comprehensive. End quote
from al-Sharh al-Mumti’.  

Thirdly: 

It is
mustahabb for the person who is doing ghusl to do wudoo’ at the beginning of
his ghusl, but if he does not do that and he pours water over his entire
body, that is sufficient and his ghusl is valid. He may rinse his mouth and
nose at the beginning of ghusl or at the end or in the middle, because doing
things in a certain order is not required in ghusl. 

See
al-Mughni (1/140). 

And Allaah
knows best.