HELP! Having issues with weightloss and diet... maybe?

I would say to give it another week. We all want fast results, but unfortunately it rarely works that way. Taking your post at face value, it sounds like you are on the right track, but just need to be a little more patient. And just for a bit of perspective... some weight fluctuation is very normal, up to 5lbs or more for some people. I wouldn't worry about 1lb here or there.

All that said... how confident are you in your estimates/logging? Are you weighing/measuring what you eat? Is your daily calorie goal reasonable? Are you logging your exercise and then eating back those earned exercise cals?

Lastly, consider using a weight trend app (I use Libra on Android) - it'll track your individual weigh-in numbers and create a trend... this helps take some of the emotion out of the individual numbers and help you see what's actually happening. Long term trends are MUCH more meaningful when using weight as an evaluation of progress.

I have been logging consistently for over a week. I began really trying about two weeks ago.

It's going to take much longer to have reliable results. Think in terms of months rather than days and weeks. Weight can fluctuate up and down a lot day-to-day. Try downloading Libra or HappyScale apps to trend your daily weigh-ins to keep focused on the big picture.

I have given up regular soda

If you can fit your favourite sodas into your daily calorie goal, there's no reason to give them up. If you're equally happy with other beverages or diet sodas, saving those couple hundred calories for solid foods is a good option.

I stopped snacking at night

Meal-timing is irrelevant for weight loss. I personally like to skip breakfast so I can snack more in the evening. I don't like going to bed feeling hungry so I stack my calories later in the day.

I began drinking more water and eating fairly clean.

Increasing water intake is fine if it was low before. Eating "clean" isn't necessary for weight loss, you can continue eating whatever you want within your calorie goal. I eat plenty of desserts, fast food and junk food and still lose weight at a very steady pace.

I have been a deficit for my calorie intake every day and I am also working out for at least 30-45 minutes everyday including lifting weights.

Are you tracking your solid food intake with a scale, and liquids with measuring cups? How are you calculating your exercise burnt calories? The more accurate you get, the more reliable your results will be. People often overestimate their workout burnt calories and underestimate their food intake, leading to slow results.

I feel like I have been a saint about my diet and exercise, but somehow I gained a pound in the last week. I run around like crazy, I am a mom of two young boys.

It's only been a week, woman! That pound you gained is most likely water weight from your new strength routine. Water weight can also be caused by menstruation/hormones, salt intake or stress. You can also register a higher weight if you have poop/pee in your system. There are tons of variables at play, a pound gained is meaningless in the big picture.

I am just getting nervous that this won't make a difference. Of course, when I feel defeated I want to just eat whatever. It makes it difficult to stay on track.

Be patient, keep doing what you're doing, and look at your losses in a month's time. Averaging a pound lost a week is a fantastic pace for most people, so keep your expectations realistic. Good luck!