I have a question How I make that mom ask me to catch latios or latias..

She already did. Remember when she asked you what colour the creature she saw was?

When latias is in one place, try not to use fly because ones you arrived there it will be in another place, just walk and surf to find her, also just use a super repel since she's only at level 40.

Ok heres an answer for you. You already have latias appearing to you, so you don't need to talk to her. And latias moves when you fly, so it's very hard to find her. So an easy way to find her is to keep flying to mauville, until latias is on a route next to mauville. When it is, you must predict what route it will then move too. It's a long process, but it works.

You only have one chance to chose Latias or Latios.
Whenever you fly somewhere, Latias will also fly somewhere completely different.

Well it's good that you've found him, he appears in random places but make sure you have a Pokemon that knows mean look in your party, but just keep looking in you poedex and try to walk to the place that he is near then he should appear.

The problem you are facing is that when you change your location, so does Latias! Any time you go in/out of a building or change routes, Latias will also change it's spot, so you'll always be a step behind it. It would be easiest to run into again by finding a location where you can easily change routes and there's grassy areas close by with lower than level 30 or so Pokemon generally, put around a Level 39 Pokemon in lead-one with a trapping move or ability would be helpful! Keep checking on where it is, change route, check again, and keep repeating until it appears in your area-once it does, stay in that area and keep using max repels until you encounter it again-it shouldn't leave that area unless you change routes/cities or enter a building. Be ready this time since it probably caught you off guard the first time, weaken it with the right team and have plenty of Ultra or Timer Balls in your bag. Hope this answers why she's never there when you get there...good luck!

Once you've found her it's a lot easier, trust me. I'm not sure if she moves in a certain pattern, but do what the one guy said, keep flying to muville, and go either to the west where the day-care is, south below cicling road, or north in the desert. I personally would not go to the desert, because she gets hurt there. Also, try putting Wobbofet or Wynot first in you're party because of their abilty. Good luck!

Are you going inside caves or buildings? Latios and Latias never appear indoors(whether in a cave or in a building). Every time you enter a structure, they move to another spot on the map. Remember, it's a matter of luck and timing to encounter Latios or Latias.

Are you flying to where she is? Don't, walk or use your bike. Also, don't go inside caves or buildings when you are tracking her down. When you fly to where she is, Latias will go to a connected route. And if you have a lot of money, buy as many Max Repels as possible. The repels only keep basic Pokemon away. When you battle her, put her to sleep and when you damage her it will be the same the next time if you don't catch her the first time.