Ur moms visit visa valid only for single entry, once you leave the country you got re stamp the entry visa. Basically she cannot visit Dubai once she entered to Qatar.
But you can do other way around, ask your mom to get a ticket to Doha via Dubai, (she needs to apply for UAE visa, you can do through a hotel, that’s not a problem) so she can go to Dubai directly from your country & come with u’ll to Doha