The person from Day Centre will have met many people like your MIL before. They usually have ways of wording things.
My husband hates going and sometimes digs his heels in. When I rang last December once again to say he said no, I thought they might say we will take him off the register, but no they said we will keep his place open, after 3 weeks they would come out to vsit him and try to persuade him to go back, and it is only after 6 weeks in a row of saying no that the place is removed.
Even if he was to say no 5 weeks in a row but went the next time. the 6 weeks starts again . In other words they really try to encourage people to go.
Tomorrow if my husband says no will be the 4th in a row, but at the moment he is talking as if he will go we shall see.
Good luck anyway
Jeannette