You have a foolish tenant on several counts. She rents a place one mile from the ocean and then cannot cope with a rare hot weather spell. (Americans seem increasingly unable to make rational dicisions based on real probablilities, real risk, actual costs and actual benefits.) Then she panics into offering $thousands to fix what is surely a temporary problem. To prove that she thinks with her heart instead of her head, she says this is “for the children”, a phrase that invariably comes from a superficial thinker. Instead, the $thousands she is offering should be put away for her dear childrens’ college fund, or more likely the drug rehab costs.
You have not mentioned that a husband is involved here, so I’ll make the assumption one is not present. If he were, he’d likely bring her down to earth on her spending decisions. OK, a sexest assumption on my part, but I’m sticking to it.
If you take her foolish money for central AC, it will come back to haunt you with guilty feelings. And what if she puts up the money, you schedule the install for early October, in the middle of a cold spell? Thereafter normal San Diego weather kicks in all fall, winter and spring, and she gets bitter for handing you that capital improvement that she doesn’t need after all. Trust me, she will find a way to blame you.