To some it is difficult to understand that ones sex and sexual orientation are not the same. Many see transsexualism as "a guy/girl becoming so gay that they want to be a girl/guy" which is far from the truth. With a lack in understanding of homosexuality, I could see how people can make that connection, even though it is not true.
You should ask your mother "Gay men are gay men. If they became women, they wouldn't be able to be with gay men anymore, because gay men like men, not women. Not even men that look like women."
And if that doesn't work, then ask "Going through with transitioning is leaps and bounds tougher to go through than it is being gay. Why would someone transition in denial to being gay? Logically, someone would use being gay as denial of having transsexualism."