The usage of "to get to do something"

Question

Could you explain what the highlighted parts mean please?

An added benefit of Valerie's schedule is that it corresponds closely to her 13-year-old daughter's schedule, which means they have more time to spend together. "I love that I get to see her first thing in the morning, and make breakfast for her," Valerie says. She also hopes that her good sleep habits will rub off on her daughter, and that she will grow up with a healthy appreciation of sleep and its importance. "I certainly don't take sleep for granted like I used to."

If " to get to do something" means "to begin to do something" , can we use it in both forms :

For example :

I love that I get to see her first thing in the morning

I love that I get to seeing her first thing in the morning

Because a source says it should be used ing form after get to

get to doing something to start doing something

He got to thinking that it was all his fault.

Answer 1

The phrase "get to do something" implies to have the opportunity to do something. So the meaning of the first sentence is "I love to have the opportunity to see her first thing in the morning".

The phrases "get to do something and get to doing something" aren't interchangeable to convey the same meaning. The latter phrase means "to start doing something such as I got to talking to her. I got to thinking that it was his fault.

Both the sentences are grammatically correct, but they convey different senses.