You are making a classic error here. The 10th plague was the death of the first born... of whatever age... not just infants or children. If I recall correctly it wasn't just the first born of humans but all domestic animals as well.
Khanaferre Sobekhotep IV is identified by Rohl (not Roth) with the Pharoah of Moses birth, not the Exodus. The Exodus, according to Rohl, occurred 7 Pharoah's later under Dudimose who may have also been referred to as Thutmose.
In regard to the mass graves found, Rohl's reasoning was that something occurred that required quick burial with little or no regard for religious niceties. The burials are numerous and indicative of some catastrophe where the sheer numbers of dead overwhelmed the religious burial system.
Unfortunately, the Egyptians didn't adopt the war chariot until Dynasty XVIII, post Hyksos; this is attested by inscriptions and wall carvings that are independent of chronology.
This is proving to be possibly erroneous.
German Scholar Wolfgang Helck reports a portion of a 13th Dynasty stele shows King's son and Commander of the Edfu Army, Prince Khounsuemwaset, and his wife seated in chairs. Under her chair are emblems indicating she is head of the household... and under his chair are a pair of Charioteer's gloves indicating he was a charioteer. The Charioteer's gloves were used in later carvings to indicate rank and were also distinctive on later carvings showing actual charioteers. The father of this charioteer prince was Dudimose. In addition, the remains of domesticated horses have been found in strata associated with the 13th dynasty.
Incidentally, distinctly Hyksos graves have been excavated with horses ritually sacrificed at the head of the buried person. This may indicate that Hyksos also had horses and hence, chariots.
The conventional explanation is a simple plague, which seems to fit the evidence - mass graes, hasty buriel, the settlement subsequently deserted. That's a classic scenario.
On the "charioteers gloves" claim, I just think that's too far-fetched. A picture of a charot would be convincing. But the symbolism of accoutrements changes over time, so for all we know those gloves may have indicated social rank or something. After all, modern air force officers wear many accoutrements that predate the invention of powered flight.