Sounds like you have two problems:
1. Unwanted plants in your flower bed.
2. Flower bed up against house needing protection from
insect infestation.

1. There are those fabric type soil covers that you roll out over the soil and then cover with gravel, mulch, or soil. You can also have someone rototill the entire flower bed cover the bed for a season and let it all rot then
remove the cover and replant but this will not solve the problem of unwanted seed from falling into your garden!
Spot weeding seems inevitable or elimination of the shrub/tree that is causing the problem may be the easiest course to go??

2. You need to set up a solid barrier between the house's foundation and the flower bed. perhaps a path between the two. use the ground cover liner as described above and gravel is one option. it all depends on what your fancy dictates.

hope this helps. cheers.

There was a rumor that spread across the internet like wildfire this spring about trees blown down by hurricane Katrina were being chipped and sold as mulch. The mulch would contain the formosan termite which is a very nasty pest. The rumor was completely untrue, so I don't believe that using wood mulch properly is going to contribute to a termite problem.

If you mulch up against the house you should make sure that you are not putting it up against any untreated wood. This can let moisture seep into the structure encouraging wood rot and allowing carpenter ants or termites a way in. Putting mulch up against concrete shouldn't be a problem.

mulch doesn't really attract termites to your house.

A 3 year old could be taught to help mom pull weeds in the flowerbed.