I do agree that a screening for Type 2 diabetes should be done for most people over 40 as part of their general check up, *especially* if you:
-Have a family history
-Are overweight
-Have evidence of the metabolic syndrome, such as high blood pressure, excess abdominal fat, and/or high cholesterol
-If you take any Rx medication that may increase the risk of developing Type 2 diabetes, such as steroids.
There are other reasons, such as if you have a rare medical condition that can cause a temporary increase in blood sugar, such as Cushing's Disease. In most cases, any increase in blood sugar will go away when the underlying disease is treated. However, your doctor (if a good one!) will know to screen you in this case.
I do think that you should feel comfortable asking your doctor for a simple fasting blood sugar as an initial diabetes screen. You may want to say that you have a family history, and you have been having some symptoms of diabetes, such as excess thirst, etc. This may not be the case, but it will trigger your doctor to order the test!

You didn't hear that from me though....hehe...
An *oral glucose tolerance test*, or OGTT is the best way to diagnose any sign of abnormal glucose tolerance. If you are in the "higher risk" category (i.e. your mother has diabetes and you are overweight), or your fasting blood sugar is even slightly abnormal, an OGTT should be done without question.
It's not a bad idea to use a relative's blood glucose monitor, just make sure that you have been shown how to use it properly, otherwise you may get abnormal results. Also, although a home monitor can "screen" for diabetes, keep in mind that they are not considered accurate enough to officially diagnose Type 2 diabetes. A venous fasting blood sugar test, an A1c test, and the OGGT are the gold standards.
Perhaps in your case Fizz, you might want to go for a free "diabetes screening" offered by your local ******** (i.e. Wal-Mart) or clinic. These are offered quite often now by the larger pharmacies. Some pharmacies even have Certified Diabetes Educator Pharmacists and/or weekly diabetes clinics staffed by nurses with diabetes training. They may test your blood sugar for you for free at your request. You can look in the phone book and call around. You have nothing to lose by asking! Also, you can buy your own meter fairly cheap. However, nothing can replace a professional's help if you are new to the diabetes scene.
If you are *really* in a bind, you can buy cheap urine glucose dip strips without a prescription. The problem with this is that they are not very accurate at catching a high glucose level unless it is already quite abnormally high. For this reason, not the best choice, but still an option. Having a negative result here doesn't rule out diabetes, but a positive test signals that you need medical care right away.
Your doctor may have decided not to screen you because he may feel you are not at exceptionally high risk for diabetes yourself. For example, if you are younger, thin, active, follow a healthy diet, and have normal blood pressure, your doctor may not feel that you are at a high risk for Type 2 diabetes, even if your mother does have it.
I am *not* saying that you should not be screened, just that in your particular case, your doctor may not feel that your profile warrants a screening if you have no symptoms, especially if you are under 40. In many (but not all) cases, Type 2 diabetes is often tied to lifestyle (obesity, excess food consumption, lack of exercise) and increasing age rather than simply genetics. That's not to say that genetics don't play a role, just that the genetic risk is higher in some families and people than others.
If only your mother has Type 2 diabetes, developed it at age 75, and was overweight at the time, than your genetic risk is *presumably* lower than someone whose entire family developed Type 2 diabetes in their 30's, and despite being thin and eating healthily etc. To summarize, you risk is increased because you have an increased risk of carrying the genes for Type 2 diabetes, but you may not have as *strong* of a tendency as someone whose family has multiple cases. Especially if those cases seemed to not be tied to a high risk lifestyle.
I would like to point out that sometimes it is the *lifestyle* that is shared by a family that contributes to Type 2 diabetes in some cases (but not all of course). For instance, it may be that the entire family eats larger portions and junk food often and exercises less than they should, leading to obesity and Type 2 diabetes, rather than simply family genetics.
Many people can have the genes for Type 2, but never develop it if they work hard at a healthy lifestyle. Research has shown that a healthy lifestyle can delay and even prevent some cases of Type 2 diabetes. In some cases, you do NOT have to get it! The course of Type 2 diabetes can be modified in many (but not all) cases. If you have any of the risk factors (excess weight, high blood pressure, etc.) and a family history, you doctor should refer you to a "chronic disease prevention program/healthy living program" to help you try to prevent developing Type 2 diabetes. This can be done with diet, weight loss, and exercise.
Even if your test results are normal, you should still strive to follow a healthy living program, which usually includes a visit to a dietitian. You have a lot more power to control your destiny than you think. Many people think they are "destined" to be overweight or develop Type 2 diabetes, when this is not always the case. You don't have to become a size 6 or run a marathon to reduce your risk of Type 2 diabetes. Small things make a huge impact. Of course, not all cases of Type 2 can be prevented, but don't you think you deserve to give yourself the best chance?
Go get screened ASAP, and then go from there! Good luck!
Note: This information applies to "general* Type 2 diabetes cases only. This information is NOT relevant to MODY, Type 1 diabetes, LADA, the KIR 6 mutation monogenic diabetes, etc. These forms of diabetes are not preventable.