SDP entitlement

Would me or my mother be entitled to SDP as we both get PIP enchanced care and mobility and are in ESA support group, i know you must live alone but would i not be an exception since i am also getting full disability? we got a paper to check our eligibility today which was asking if anything had changed since 2015 which was when my mother first was qualified for pip and I am getting it since 2012.

Thank you Gordon we sent my mothers is10 and wanted to ask a few questions since I am uncertain about this.

1 will my mothers IS10 give us both SDP, if not should i phone up or let them sort hers out first?
2 will we both get back payments from 2015?

That's a shame since I was told it was only possible to get if you lived alone and did not know about the exceptions until you explained it, i don't know why this payment is so hidden and not explained properly for the normal person as its something that they claim is automatic even though they cant figure out that two people living together and getting the same welfare are eligible. I will call them up tomorrow and see what happens.