Lets see the the P-38 was removed from service in Europe because it was expensive to maintain and the mean hours between failure for the Engines and some of the other components that made it hard to maintain in England. Add in that the P-47, P-40, P-51 and the Beaufighter were already in the USAAF supply stream for Europe, so to simplify as the P-38 wasn't the end all in fighters against the Me-109 and FW-190's. So they were slowly removed from service in places like England. It was still used for a while in the Italian area of operations before it too was replaced by the P-47 and P-51 for the most part. That was one of the reasons it thrived over in the Pacific, is that most of the supply streams were still being developed so it was easier to start one going from San Fran to Hawaii to Oz to NG or the 'Canal was because there weren't already a number of competing supply streams as it was. Add in the fact that for a number of the units that were in the Pacific for the first 18 months were units trying to hold the line (the P-400, P-39, P-40) it was easier to phase those units as and start up the P-38.
As to the Bf-110, remember for a while there was in everyone's thinking two (or even three) different types of fighters in the air force inventory. Pursit planes which would engage other fighters and light bombers, heavy fighters/interceptors which would engage the bombers and then was the question of should interceptors be a seperate category by themselves. Anyhow, the Bf-110 when bought was going to be something like the Boulton Paul Defiant was thought of, in that a plane which would be able to have the range to intercept enemy bombers far enough from the target to allow most of them to be downed by both the forwrad firing guns and if needed the rear gun. However, during the build process like a number of aircraft have seen, the German high command of the Luftwaffe changed the specs from just being a fighter to being a fighter bomber with certain other aspects to it the contract change. Which adding the equipment to give the airplane the ability to deliver bombs and perform dive bombing adversely affected its weight and adversely affected its manuverability and speed.
The Mosquito was adapted to a fighter from the successful bomber and did well in this course. Its ultimate evolution was the Hornet aircraft which very successful in the post war period between the demise of the prop engine and the introduction of reliable jet engines. Beyond that I really think that the Beaufighter was a successful twin engine fighter in the Commonwealth Air Forces. It did yeoman's duty in all theaters and did it well, whether it was battling German patrol aircraft over the Norwegian seas or down along the Channel protecting the various inter-coastal supply convoys from both surface and air attack. In the Pacific, it did wonders in SE Asia and when introduced in the SWPAC region they finally had a fighter which could escort all the way from PM to Rabual and back or further in some cases.
The US had the P-38 already talked about, but then we had the XF5F which didn't provide the performance promised. Then there was the YFM-1 which sucked The P-61, P-70, Beaufighter, P-82, F7F as it for twin engine fighters before the whole idea was dropped with the arrival of Jet engines and the early ones having the requirement of twin engines due to questions about reliability.
A lot of what killed the early twin engine fighters was the engines and the mission creep that was added to the aircraft. The pre-war engines were just not being successful and delievery of the performance as envisioned by the engineers designing some of these aircraft. If we again add in mission creep, that is an aircraft is designed for one mission but someone wants to add another mission. Whether that is being a level bomber or a search asset or what. To add some of the extra equipment, even if it isn't installed all the time, adds weight and puts a drain on the performance of the engine. Bad Performance of the engine leads to bad aircraft in certain situations.
Take my word for it. You never want to be involved in an “International Incident”.