It's very likely that Alice is Ann's child from a prior marriage.

1.  Marriage Record:

2.  AIS (Accelerated Index System) Census Index (online at Ancestry.com):

1859 State Census

McGRAW

Patrick

KS

Leavenworth Co.

St. Ranger Twp.

p.   4

The Kansas State censuses were in 1855 and 1865, not 1859, but there was a Registration of Voters in 1859.  So, which is wrong, the date or the title of the database?  And it's Stranger Township, not "St. Ranger."

3.  1860 Census Images (online at Ancestry.com; Image #65 of 133):  Leavenworth City P.O., Leavenworth City 2nd Ward, Leavenworth Co., KS, PN 65, 632/583, enumerated 9 Jul 1860 (extracted by Diana Gale Matthiesen):

Wm Philips	39	m		Saloon Keeper	2000	200	Ireland
Julia	30	f					Do
Mary Ann	7	f					Kansas
Patrick McGowan	25	m		Bartender			Ireland
Margaret Philips	7	f					Ill

The informant must have been one of the PHILIPSes who didn't know Patrick that well because s/he got his surname and birthyear off; yet, it's very likely that Patrick "McGOWAN" is our subject.  They are living three households down from saloon keeper B. CEBAILLAC (of France) and bartender James GILL (also of France), who are living next door to bartender William SHEHAN (of Ireland).  Leavenworth must have been some frontier town!

4.  1870 Census Images (online at Ancestry.com; Image #277 of 853):  Hotel, Leavenworth City, First Ward, Leavenworth Co., KS, p. 267A, PN 11, enumerated 2 Jun 1870 (extracted by Diana Gale Matthiesen):

1870:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

10

11

12

15

16

17

19

51

60

McGraw Pat

40

M

W

Saloon Keeper

4000

300

Ireland

/

/

/

______ Ann

38

F

W

Keeping house

Ireland

/

/

______ John

16

M

W

at School

Indiana

/

/

/

______ Ann Maria

11

F

W

at School

Kansas

/

/

/

Gresmon Allice

18?

F

W

adopted

Indiana

/

/

Walsh Edward

45

M

W

Hotell Keeper

400

50

Ireland

/

/

/

_____ Margaret

35

F

W

Keeping House

Ireland

/

/

_____ Thomas

11

M

W

at School

Kansas

/

/

Connelly N P

22

M

W

Bar Tender

Ireland

/

/

/

Quess? Margaret

22

F

W

Cook

Ireland

/

/

/

/

Baldwin Matilda

49

F

W

House Keeper

Ireland

/

/

/

Neal Mary J

13

F

W

Domestic Servt

Texas

/

/

/

/

[23 lodgers, all single working men, mostly in their 20s and 30s]