How can i stop our sump pump in the basement from sucking the water out of the P traps in the bathroom?

If the system was initially installed correctly and it worked before, there is no way a sump pump could be sucking a sewer system P trap dry. They are two separate systems.

If you are talking about a sewage ejection pump in the basement sucking a P trap in basement plumbing fixture dry, that would be possible if the vent provisions for the ejector pump have been plugged. It would be unlikely the ejector pump would empty a P trap on the upper floors in that the upper floor sanitary drains normally flow by gravity to the collector sewer.

Make certain the venting for the ejector pump / sewage holding tank has not been compromised.

This is a workable theory if your problem is indeed the water table rising. If you have had a lot of rain, don't overlook the possibility that your water table is still below the floor, but the water is running toward the foundation in the locations where you are seeing water seeping in. Check the slope of the ground outside the house, and note places where it appears flat or sloped toward the house where it meets the foundation. Get some topsoil and add dirt to the areas that are low, being sure to compact the soil to encourage water to run off it away from the house. Be sure to provide a path well away from the house where the water can either seep into the ground or reach a storm sewer system or french drain. Be sure the gutters are clear and the downspouts are in place and routing water away from the house as well. If all that is in place and you still have seepage, then you may indeed wish to have the sump system installed. To do this they generally will jackhammer a trench around the interior side of the basement walls and install gravel and drain tile. the drain tile leads to a sump hole and the sump pump has a floating switch that will kick it on when the water in the hole rises to a certain level. the pump has a pipe for ejecting the water out to the back or side yard, again routed far enough away to have the water run away from the house.

Wow sounds like you roof vent may be clogged or less noticeable the vents in your sink are clogged or both coach. Anyway when this was put in did it get vented properly to the roof you will only know if you can 1. see the vents which there should be since they are required. The P-trap is supposed to prevent that from happening is your sump pump running all the time.You sound like you have more than one problem but both may be related. In the sink there are vent holes sometimes a wet vac set on blow will blow that nasty stuff out of the sink ha ha it will make a mess if you don't watch it.I mean stuff will fly everywhere. The second thing you probably will have to do is find the roof vent and snake it out. Once the roof vent is unclogged you should be done with the smell which a properly working p-trap will prevent. You didn't give us any information on your place so I can only assume your in a standard single family ranch style house or something like that. Think single floor with a basement also you don't tell us anything about your roof that could cause a problem so a plumber comes to mind. Also do you have a sewer service or a septic tank. They may be related to your problem.

It should not be possible for that to happen.

The sump pump removes free, ground water from under the basement floor.

The "full level" of a trap is determined by piping heights and angles.

They are 2 separate systems.

I'm not saying your diagnosis is wrong, but it is extremely unlikely.

The only way that could happen is if your sewer pipes are not completely sealed, which is not that uncommon in older piping. Many older pipes were made of clay or cast iron which don't seal well and crack. Even newer PVC is vulnerable. You would be surprised to see what a root can do to plastic pipes. If they crack, then your home plumbing and ground water have a cross connection which would allow your sump pump to suck water from your home drainage/plumbing system. A plumber can run a smoke test to check for bad joint, breaks in pipes, etc.

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You need to install a check valve it will stop the back flow issue