Which visa ?
My partner is from Laos. She has two young children from her previous Thai partner that therefore hold Thai citizenship. Both the children reside with us. My partner being Laos still does visa runs on a monthly basis to stay in the country legally. It's not a major issue at the moment as we reside in Nong Khai, but we are looking to purchase a house in Hua Hin. I am on a retirement visa.
Is there a visa that my partner can obtain on the basis of her being the children's mother and them being in her sole care ?
Can only suggest when she does a border run , im guessing over the Friendship Bridge, she can go into Vientiane and inquire at the Thai Embassy, not the answer your looking for but they should be able to provide it.