So I downloaded the image from Twitter and opened it in Photoshop for a close examination.
I do not believe his daughter was present for this photo. Reflections in the mirror have nothing to do with my conclusion. Furthermore, I also do not believe his wife was present. I believe he was actually alone for this photo. Perhaps it is a composite, but I do not believe this is an undoctored image.
I have labeled the points of interest in the attached image from 0 to 9. These labels are the only alterations I have made to this image. Here is the .psd file resulting from my labeling for any skeptics to compare to the original as posted to Twitter.
LABEL 0: Circled area contains a pixel-perfect vertical color border and obvious blur tool artifacts.
LABEL 1: Circled area contains what appears to be the paper wrapper of a straw. I've circled this item to call attention to the shadow beneath the paper, an expected feature when the paper is of three dimensions (in other words, not flattened into a strip) after removing the straw. Note that this item, by itself, is not out of place unless compared to the item in label 6 (below).
LABEL 2: Circled area contains a portion of the jewelry worn by Pence's wife. Notice that one of the links, the border of which should extend to cover a small area behind which the table can be seen at the item in label 3, is in fact completely missing, as if it had been sliced off that link of the necklace. Upon closer examination, the color values for the necklace links which should appear at that exact location are completely absent.
LABEL 3: Compare to the item circled in Label 2 to observe the expected thickness of the missing portion of the link expected of the item in label 2. The item in this area and the item circled in label 2 are not consistent given the type of necklace and the angles of the links relative to each other and to the background.
LABEL 4: Circled area contains a very sloppy blur operation during compositing, with the color values of the well-defined edge of the table vanishing into the color values of the shadows at the exact point of where the composite would meet the edge of the table, only to become again well-defined further up the edge into the "rear" of the photo.
LABEL 5: Contains two pixel-perfect lines of dark color, one horizontal and one rotated exactly ninety degrees to vertical, which appear to be intended to be a curl of hair. Also note the lacy pattern of the top of the blouse, which eliminates the lace as a possibility of the origin of this artifact.
LABEL 6: Contains what is in my opinion the most egregious telltale in the image. The circled area contains the wrapper of a straw as in the item found in label 1. However, note that the expected shadow is in fact completely missing, not only from the table top, but also missing from the edge of the table at the location this item overhangs the edge. Given the angles of light involved, and regardless of whether the paper tube had been flattened or not, a shadow falling across the forward edge of the table is expected and is completely absent.
LABEL 7: Circled area contains another sloppy blur operation following image compositing. In this case the doctoring is even more obvious; the color values of the slight reflection of light along the bottom of the forward edge of the table simply vanish when they should not, only to reappear along the edge as the edge moves from left to right. Very, very, very sloppy.
LABEL 8: Circled area contains YET ANOTHER sloppy blur following image compositing. See above.
LABEL 9: Circled area contains a pixel-perfect vertical line at the edge of the image composite. In this case, no effort at all was made in even as much as a cursory attempt to properly blur the edge following compositing.
Feel free to take issue with my observations.
BONUS: Look at the reflection of head of the woman on the left. What is the lump sticking out from "behind" her head in the reflection?
EDIT: BONUS 2: The standing vertical angle of the left-hand drink glass in the foreground of the image is very, very slightly rotated off of true. May be something, maybe not. Doesn't look right.