grammar - When referring to herself, is there any pronoun other than お 母さん when speaking to her children?

Consider the following conversation quoted from a textbook used in my class.　鈴木 is the mother of 鈴木伸.

鈴木：伸ちゃん、お母さんが試着{しちゃく}している間、ここで待っていてね。

鈴木伸：うん。

In my understanding, お母さん is used to refer to mothers of other persons and 母　is used to refer to the speaker's own mother. So 母 is not possible in this case.

When referring to herself, is there any pronoun other than お母さん when speaking to her children?

Answer

The short answer is that the list would be somewhat long if not endless.

Why so? Because whatever word a kid uses to address his/her own mom with, the mom will use that word to refer to herself with as if it were a first-person pronoun. You would almost need to forget English to appreciate this phenomenon in Japanese.

(Your second paragraph from the bottom worries me slightly because, frankly, the 母{はは} vs. お母{かあ}さん issue has nothing to do with the matter.)

How kids address their moms differ from one family to another. The more common words would include:

「お母さん」、「母さん」、「おかあちゃん」、「かあちゃん」、「ママ」, etc.

None of these are "pronouns" by the book, but regardless of what dictionaries may name them, they are used just like first-person pronouns in real life. When speaking to their own kids, moms use those words to refer to themselves while the kids are young.

When the kid reaches a certain age, the mom starts using a "real" first-person pronoun such as 「わたし」, 「あたし」, etc. to refer to herself when talking to her own kid. When that happens, again, differs from one family to another.

In my own case, my mother, who had originally referred to herself only as 「お母さん」 when talking to me, started using a combination of 「お母さん」 and 「わたし」 while I was in high school and she completely switched to 「わたし」 after I graduated from high school if I remember correctly.