I think I'm falling in love with my girlfriend's mom
That feels very improper. Why do you think you're falling in love with her?
I think that women look better when they are getting older, and also I'm going to break up with my girlfriend.
We can't always control who we're attracted to, but we can control the actions we take. Pursuing your girlfriend's mother is very inappropriate, even if you already plan on leaving the relationship. People frown on others who go out with their exes parent, so you should avoid getting in a relationship with her.
If I break up with my girlfriend, she'll never let me see her mom again.
If you really want to break up with your current girlfriend to date her mom, then you can do so, as it is better than dating the both of them. It is still strongly frowned upon dating people with a huge age gap so I do suggest you prepare for any backlash with that.