Just keep your son in his crib, until YOU feel, he needs to come out.
Your son is only 1 years old.
That's fine.
Don't change your plans, just because MIL is offering a bed.
Do what YOU think is best.
My son, slept in his crib and loved his crib and slept well there, until he was even 3 years old. Then HE told us, he wants to come out and sleep in a bed. So, he does now. A mattress on the floor. He moves around a LOT during sleep, so having a mattress on the floor is best for him. He sleeps fine. He was ready for that.
Do what YOU think is best....
You can still take the mattress from MIL and then just store it upright against a wall or somewhere and maybe use it when you feel... it is best. You don't have to, use it RIGHT then. I personally, would want a NEW unused, mattress. I would not want bug infestations etc.
I wouldn't put your kids in the same bed.... and since your daughter is a "thrasher" in her sleep. I wouldn't personally, want to sleep with a 'thrasher.' It would disrupt my sleep and irk me. AND then "I" would not get a good sleep. I wouldn't want to get sleep deprived, because of the way the other person sleeps.
good luck,
Susan