My brother and I want to invite our mother to visit to Canada. Is it a good idea to have two letter of invitation stating that my brother will cover 50% of the expense and I will cover the remaining 50% of expenses?
You can include one invitation, co-signed by both of you.
The letter need not specify a 50-50 split in paying for your mom's expenses. You can explain that both of you will support her visit (accommodation, travel and living expenses, travel medical insurance although not necessary, etc)