Introduce the dogs to each other on neutral territory, so that neither of the dogs feels the needs to defend it's "home turf" against an "invading stranger".
Take your maltipoo with you on Thursday, and give him a nice 30-minute walk to tire him out. Then when you take the terrier out of her cage, take both dogs for a walk. Don't let them meet face-to-face at first. If you walk the maltipoo on his leash, and your mom take the terrier on her leash... walk in the same direction together - but 6ft feet apart - for 5-10 mins
Make sure the dogs don't have any behaviour problems with each other, and gradually you & your mom come closer and wak side-by-side for 5-10 minutes. Once the dogs become indifferent to each other, then let them meet and sniff each other.
When you return to the car, you sit in the back seat with the terrier. Make sure the maltipoo sees that you have allowed the terrier into the car, and then allow the maltipoo into the car.
This is the time to be aware of any initial 'aggression over territory'. Don't be tense or nervous, try to stay relaxed.
(it may be a good idea to have a travel-crate in the car, just in case you need to keep them seperate).
If the maltipoo settles in the back of the car with you & the terrier nicely, your mom can then get in the front and drive home. If there is any sign of aggression, remove both dogs from the car and repeat the walking together again for another 5 min before returning to the car again.
When you get home, repeat the exercise of walking both dogs around the block for 10 minutes together before you go into the house. Take both dogs into the house together.
Keep them both on their leashes and walk them both around the house & garden, to show the maltipoo that the new dog is to be welcomed.
Have a new dog-bed & new food bowl for the new dog, to prevent the maltipoo getting annoyed at the new dog taking HIS bed & food.
Make sure you supervise them playing with toys, to correct any fighting over toys, teach them to share the toys.
Feed the maltipoo first, so that the terrier doesn't try to steal his food.