Oh God… “me and my children”… it’s making me cringe reading it. That sounds SO wrong!
I found this quite useful as a guide (remove other people in the sentence):
Errors in Usage
Beginners often confuse “I” and “me” because they mean the same thing, but even native speakers can struggle when there is more than one subject or object. Study the errors below so you can avoid making similar mistakes in your writing.
Jack and me got home late.
In this sentence, there are two subjects “Jack and me,” but me is the objective case. As it’s a subject, the correct pronoun is “I.” A good way to check is to remove the other people at the beginning of the sentence and re-read the sentence to see if it sounds right (“Me got home late” does not!). Most people can find the right word by ear this way.
The puppy licked my sister and I.
Here “I” is used as a direct object-the person receiving the licks but “me” is the right word to use as a direct object. Again, try removing all other people after the verb except “I” and re-read the sentence to see if it sounds right (again, “The puppy licked I” does not sound right).
The snobby girl thinks she's above my family and I, but she's not.
This is another example of how multiple objects adds confusion. Here “I” is incorrectly used as the object of the preposition “above,” but it should be “me.”
It wasn't me.
This one trips up a lot of people as it can’t be checked by ear, like the examples above. Though this is a common colloquial phrase, it is not grammatically correct. In this sentence, “was” is a form of the verb to be that sets up a predicate nominative, so the writer should use “I,” which is in the nominative case.
Suzy and me are best friends.
This is another example of an error because of a plural subject. “I” should be used because it’s the correct choice when it comes to subjects. It can also be helpful to consider the position of the word in the sentence. “I” is used before the verb, while “me” is almost always used after the verb (the exception being the predicate nominative).