I'd be tempted to build a secure run for your mum so she can't let your dogs out.
My dog sleeps while I'm out - she's fine with that. She gets one or two good walks plus a lot of trick training every day so that helps her be restful between times. I think I'd freak if she decided to take herself for a walk and she's not given the opportunity.
I would not give either dog the opportunity to go wandering - there is just too much that can go wrong. From bad people to bad traffic or just wild life accidents.