Houston I90 TRACON Controller reported an NMAC and stated handoff communication issues with ZHU Center contributed to the event.

Narrative

I will start out by saying that all three of these aircraft go to the same point and descend to the same altitude; I then give them all to the same controller within our core airspace. I got Aircraft X at 11;000 to cross BLUBL at 9;000; there were at 11;000 about 7 miles from the fix. I then see Aircraft Y start to flash and turn into BLUBL at 11;000; keep in mind my Aircraft X is just off their left still showing 11;000. I then see the Aircraft Z that they have right behind the Aircraft Y also lower but I can't recall their altitude. At this point Aircraft X and Aircraft Y are going to merge and might almost hit; remember Aircraft Y is a flight of two. I called the Center to and at this point I'm vomiting words to get them to pry Aircraft Y away from my Aircraft X and I'm trying to get control of the Aircraft X because it's still in the centers airspace. I thought about just cranking the Aircraft X to the EAST but then I saw Aircraft Y turn to the EAST. At this point the Aircraft Z is a mess with the Aircraft Y. The center never acknowledged what was happening and never answered the line when I was begging for control of the Aircraft X. I ended up descending them expeditiously. I finally got the center on the line; she wanted a hand off of the Aircraft Y who was now showing 8;800; which is in my airspace; I told her to slow them to 210 kt; because they had to follow the Aircraft X. The Aircraft Y checked in and were showing 270kt; I feel like they were never slowed; I told the center controller to slow them. This was a total; complete mess. I guarantee the center controller switched the Aircraft X and completely forgot about it. Then proceeded to crank the Aircraft Y in and then saw the Aircraft X. This happens all the time; where the first aircraft goes in to Never Neverland once they are switched to us. I'M SICK AND TIRED OF THE CENTER PUTTING AIRPLANES IN UNSAFE SITUATIONS AND NO ONE IN MANAGEMENT DOING ANYTHING ABOUT IT.Have the center understand that they MUST sequence to BLUBL and not forget about the first aircraft. Have the center understand that speeds have to be taken into consideration on the arrival. They will put a fast moving jet right behind a prop with the crossing; thinking the first aircraft will keep their speed up because they are high. Once the first one starts down their speed goes to nothing with a jet eating them up. This exact scenario happens all the time. It's unsafe. The controllers that work U are sick and tired of it. Once again; I'm sick and tired of sitting in briefings where the FAA tells us to not insert risk into the NAS. Here is an example of the center inserting risk into the NAS and it doesn't stop. Why can't they learn how to do air traffic control? Another example of management not doing their job; they need to manage their people. Problem is; most of the FLM's over there do not know how to work planes in the areas they are suppose to be managing.