Can me and my sister claim my mom on each of our returns if we both help with her living expenses?

[DoninGA]

No.  If neither of you are providing over one-half of her total support then neither of you can claim her as a dependent.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,300 (social security does not count) in 2020
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.

[stravoski]

What if we are each providing over one half of her expenses? Equally. 

[Hal_Al]

Only one of you can claim a dependent.

If no one person (or married couple) provides 50% of the support (for example your siblings are also sending support), then a "multiple support agreement” (IRS Form 2120) can be used, to allow you to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf

You and your sibling simply need to agree on who will claim her.  You can also alternate every year.

You can't each be providing more than half of her expenses.  At best you can each be providing exactly half her expenses.  But even that is unlikely, if she has any money of her own. 

What about the 2020 stimulus ($1200 + $600)?  Did she already get that.  If not, it may be best if nobody claims her on a 2020 tax return, so she can file for the $1800.