Should the sentence containing the word three be 3 instead. The rules states to use numbers that follow an identifying noun. I don't quite understand if "these" is considered identifying but I believe two or three should be written in words.

If I should have to be out over the next two or three days, would you check with these three for me?

Yes, they should be written out.

http://grammar.ccc.commnet.edu/grammar/numbers.htm
This is a good webpage to bookmark whenever you're facing a numeral/spelled-out-number question.

Thank you sooo much. I have searched the internet and could not find a site that explained it. You are awesome!

You're very welcome!

I usually start with their index and then look up whatever I need to learn or explain:
http://grammar.ccc.commnet.edu/grammar/index2.htm

When it comes to writing numbers in a sentence, there are different guidelines depending on the writing style or preference. However, I can explain a common guideline that can help you in this situation.

According to the general rule, when numbers are used to represent quantities or measurements, it is better to write them as digits (e.g., 3, 5, 10). However, when numbers are used to describe the order of items or to indicate a position, it is usually preferred to write them as words (e.g., first, second, third).

In your sentence, "If I have to be out over the next two or three days, would you check with these three for me?", the numbers "two" and "three" are used to indicate the quantity of days. Since they refer to specific quantities, it would be clearer to use the digits "2" and "3" in this case. Therefore, the sentence could be revised as follows:

"If I have to be out over the next 2 or 3 days, would you check with these three for me?"

Regarding the word "these," it is used to refer to a particular group of people or items. While it can be considered as an identifying pronoun, it does not affect the decision to write numbers as digits or words.

Remember that style and usage can vary depending on context and specific guidelines, so it's always a good idea to consult relevant style guides or follow specific instructions given to you.